Issuu

Level

Lighthouse

Math Basic

Edition

This book belongs to

Name

Address

Telephone

School

Teacher

Grade

Level E

Lighthouse

Math Basic Edition

PROGRAM DIRECTORS Mrs. Zehava Kraitenberg M.S.

Jane Chamberlain

Curriculum Advisor, Elementary School Principal

Master of Education, Curriculum and Instruction

Credits Curriculum Writers

Review Team

Layout and Design

Jane Chamberlain

Chaya Breindy Kenigsberg

Akiva Leitner

Middle School Math Instructor M.Ed. in Curriculum and Instruction

Curriculum and School Leadership Specialist Master in Education

Project Manager

Kelly Christensen 6th-7th Grade Math Teacher M. Ed in Administration and Leadership (K-12)

Esther Aboud

Lauren Noorparvar

Curriculum Consultant M.Ed. in Special Education

Middle School Math Educator Math Curriculum Coach K - 12 Master in Education

Keely Franklin Curriculum Developer

Cierra Henderson Curriculum Developer

Yehudis Leitner Curriculum Coordinator

Curriculum Consultant M.Ed. in Special Education

Mirko Zunic Layout Director

Freepik Illustrations

Fraydel Sharf Content Director and Editor

Miriam Shulamis Eisemann Content Editor

Yehuda Gartenhaus M.A. Elementary School Principal

Mechel Weizer Curriculum Advisor Elementary School Principal

Zehava Kraitenberg M.S. Curriculum Advisor Elementary School Principal

Lighthouse Math Level E - Basic Edition • ISBN 978-1-955773-98-0 ©Copyright 2021 Lighthouse Curriculum Inc. All rights reserved. Contact Lighthouse Curriculum: Call 718.285.7100 or email info@lighthousecurriculum.com For more information visit www.lighthousecurriculum.com Content developed in collaboration with The Reimagined Classroom

No part of this publication may be reproduced, stored in a retrieval system, stored in a database and/or published in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher. To obtain permission to use portions of material from this publication, please contact Lighthouse Curriculum.

Welcome to the Lighthouse Math Curriculum! Here’s what you’ll find in every chapter:

Introduction and overview of skills at the beginning of each chapter

Clearly coded lessons: blue for the lesson page, red for the exercise page

Daily review at the beginning of every lesson to provide review of previous skills

Learn and Connect helps introduce the concept

Apply provides guided practice as a class

Practice provides plenty of problems to practice the skill

Challenge problems for enrichment and practice

Review for every chapter

Assessment provided for every chapter

7 + 6

A better way to teach Dear Educator, Welcome to the Lighthouse Math Curriculum! What makes our curriculum so unique? Lighthouse Math uses a scaffolded approach to learning and mastering math skills. When provided with a solid foundation, students can retain more information and prepare for the next level of skills.

Instead of separate workbooks and textbooks, students have everything they need built into one place: a softcover book containing 11 chapters, with each lesson containing review, new skills, and practice. All lessons include step-by-step instructions for clarity, giving all teachers - new as well as seasoned - the tools for success. The books are custom illustrated, providing a vibrant learning experience. They are formatted in a way that each grade level can be completed successfully by the culmination of the school year. Lighthouse Math gives teachers the tools they need to teach and gives students everything they need to learn. We at Lighthouse CurriculumTM are committed to providing support and guidance to our educators. We look forward to hearing from you and are available to answer any questions you may have.

Sincerely, Lighthouse Curriculum Team

1 - 1 | Properties of Addition and

Subtraction

Solve.

DAIL Y REVI EW

4+5=

9−5=

7+3=

10 − 2 =

LEAR N AND CON NECT Addition and subtraction rules

can help us find the sum or diffe

rence.

Numbers can be added in any orde r. 3+5=8

5+3=8

8+0=8

Numbers cannot be subtracted in any order. 10 − 3 = 7

Adding or subtracting zero does not change the number. 8−0=8

Subtracting a number from itsel f leaves zero.

3 − 10 ≠ 7

8−8=0

strictly prohibited.

Fill in the blanks to make the

12 + 5 =

4. 7.

number sentence true.

+ 12

6+8=8+

+ 10 = 10 + 7

63 +

12 − 0 =

15 + 0 =

10. 11 − 0 =

= 5 + 63

11. 8 + 0 =

Vocabulary

Level E

| Chapter 1 - 1

14 + 4 =

3+8=8+

0 + 24 =

12. 0 + 48 =

Commutative property of addit ion - numbers can be added in any order Associative property of addition - when adding, numbers can be group ed in different ways Identity property - adding or subtra cting zero doesn’t change the value of a number

| Lighthouse MAT H

+ 14

APPL Y

Table of Contents

Chapter 1

1-1

Properties of Addition and Subtraction �� 16

1-2

Addition and Subtraction as Inverse Operations �� 18

1-3

Addition and Subtraction Fact Families �� 20

1-4

Place Value to the Thousands Place �� 22

1-5

Place Value to the Billions Place �� 24

1-6

Comparing and Ordering Numbers �� 26

1-7

Rounding Whole Numbers �� 28

1-8

Chapter Review �� 30

1-9

Cumulative Review �� 32

Chapter 2

Place Value and Number Sense

Addition and Subtraction

2-1

Adding Two- and Three-Digit Numbers �� 36

2-2

Adding Large Numbers �� 38

2-3

Subtracting Two- and Three-Digit Numbers �� 40

2-4

Subtracting Across Zeros �� 42

2-5

Subtracting Large Numbers �� 44

2-6

Estimating Sums and Differences �� 46

2-7

Chapter Review �� 48

2-8

Cumulative Review �� 50

Level E

| TOC

| Lighthouse MATH

Multiplication Facts

3-1

Multiplication Facts 2, 3, 4, and 5 �� 54

3-2

Multiplication Facts 6, 7, 8, and 9 �� 56

3-3

Multiplication Facts 0, 1, and 10 �� 58

3-4

Multiplication Facts 11 and 12 �� 60

3-5

Multiplication Properties �� 62

3-6

Chapter Review �� 64

3-7

Cumulative Review �� 66

Chapter 4

Multidigit Multiplication

4-1

Multiplying Multiples of 10, 100, and 1,000 �� 70

4-2

Multiplying by a One-Digit Number �� 72

4-3

Multiplying by Multiples of 10 �� 74

4-4

Multiplying by a Two-Digit Number �� 76

4-5

Multiplying by a Three-Digit Number �� 78

4-6

Chapter Review �� 80

4-7

Cumulative Review �� 82

Chapter 5

Division Facts

Chapter 3

5-1

Division Facts 2, 3, and 4 �� 86

5-2

Division Facts 5, 6, and 7 �� 88

5-3

Division Facts 8 and 9 �� 90

5-4

Division Properties �� 92

5-5

Multiplication and Division Fact Families �� 94

5-6

Divisibility Rules �� 96

5-7

Order of Operations �� 98

5-8

Chapter Review �� 100

5-9

Cumulative Review �� 102

Level E

| TOC

| Lighthouse MATH

Chapter 6

104

6-1

One-Digit Quotients with Remainders �� 106

6-2

Interpreting Remainders �� 108

6-3

Two-Digit Quotients �� 110

6-4

Three-Digit Quotients �� 112

6-5

Deciding Where to Start Dividing �� 114

6-6

Zeros in the Quotient �� 116

6-7

Dividing by Multiples of Ten �� 118

6-8

Dividing by Two-Digit Numbers �� 120

6-9

Dividing by Two-Digit Numbers with Remainders �� 122

6-10

Two-Digit Quotients with Two-Digit Divisors �� 124

6-11

Chapter Review �� 126

6-12

Cumulative Review �� 128

Chapter 7

Long Division

Fractions

130

7-1

Understanding Fractions �� 132

7-2

Writing Fractions �� 134

7-3

Equivalent Fractions �� 136

7-4

Finding Equivalent Fractions �� 138

7-5

Finding an Equivalent Fraction �� 140

7-6

Simplest Form �� 142

7-7

Common Denominators �� 144

7-8

Comparing and Ordering Fractions �� 146

7-9

Improper Fractions �� 148

7-10

Mixed Numbers �� 150

7-11

Converting Improper Fractions to Mixed Numbers �� 152

7-12

Converting Mixed Numbers to Improper Fractions �� 154

7-13

Chapter Review �� 156

7-14

Cumulative Review �� 158

Level E

| TOC

| Lighthouse MATH

Adding and Subtracting Fractions

160

8-1

Adding Fractions with Like Denominators �� 162

8-2

Subtracting Fractions with Like Denominators �� 164

8-3

Adding Fractions with Unlike Denominators �� 166

8-4

Subtracting Fractions with Unlike Denominators �� 168

8-5

Adding Mixed Numbers �� 170

8-6

Subtracting Mixed Numbers �� 172

8-7

Subtracting from a Whole Number �� 174

8-8

Chapter Review �� 176

8-9

Cumulative Review �� 178

Chapter 9

Multiplying and Dividing fractions

180

9-1

Multiplying Fractions �� 182

9-2

Cross Simplification �� 184

9-3

Reciprocals �� 186

9-4

Dividing Fractions �� 188

9-5

Chapter Review �� 190

9-6

Cumulative Review �� 192

Chapter 10 Decimals

Chapter 8

194

10-1

Tenths �� 196

10-2

Hundredths �� 198

10-3

Thousandths �� 200

10-4

Decimal Place Value �� 202

10-5

Comparing Decimals �� 204

10-6

Rounding Decimals �� 206

10-7

Changing Fractions to Decimals �� 208

10-8

Changing Decimals to Fractions �� 210

10-9

Chapter Review �� 212

10-10

Cumulative Review �� 214

Level E

| TOC

| Lighthouse MATH

Chapter 11 Addition and Subtraction of Decimals 11-1

Adding Decimals �� 218

11-2

Subtracting Decimals �� 220

11-3

Adding and Subtracting Money �� 222

11-4

Estimating Sums and Differences �� 224

11-5

Addition and Subtraction Word Problems �� 226

11-6

Chapter Review �� 228

11-7

Cumulative Review �� 230

Chapter 12 Multiplying Decimals

232

12-1

Multiplying a Decimal by 10, 100, or 1,000 �� 234

12-2

Multiplying a Decimal by a Whole Number �� 236

12-3

Multiplying Decimals �� 238

12-4

Zeros in the Product �� 240

12-5

Multiplying Money �� 242

12-6

Estimating Products �� 244

12-7

Multiplication Word Problems �� 246

12-8

Chapter Review �� 248

12-9

Cumulative Review �� 250

Chapter 13 Dividing Decimals

216

252

13-1

Dividing a Decimal by 10, 100, or 1,000 �� 254

13-2

Dividing a Decimal by a Whole Number �� 256

13-3

Dividing a Decimal with Zeros in the Quotient �� 258

13-4

Dividing Money �� 260

13-5

Division Word Problems �� 262

13-6

Chapter Review �� 264

13-7

Cumulative Review �� 266

Level E

| TOC

| Lighthouse MATH

Chapter 14 The Coordinate Plane 14-1

Patterns �� 270

14-2

Using a Rule to Make a Table �� 272

14-3

Reading a Grid Map �� 274

14-4

The Coordinate Plane �� 276

14-5

Graphing Ordered Pairs �� 278

14-6

Graphing from a Table �� 280

14-7

Chapter Review �� 282

14-8

Cumulative Review �� 284

Chapter 15 Geometry and Measurement

286

15-1

Angles and Lines �� 288

15-2

Classifying 3D Figures �� 290

15-3

Perimeter �� 292

15-4

Area �� 294

15-5

Volume �� 296

15-6

Converting Units of Time �� 298

15-7

Converting Length �� 300

15-8

Converting Weight and Capacity �� 302

15-9

Chapter Review �� 304

15-10

Cumulative Review �� 306

Level E

| TOC

268

| Lighthouse MATH

C H A P T E R

In Chapter 1, we will learn about

Place Value and Number Sense Understanding how the number system works makes doing math easier. The place value system tells us how much each digit is worth. • We will learn the properties of addition and subtraction. • We will learn about fact families and how addition and subtraction are opposite operations. • We will learn about place value up to the billions place. • We will compare and order numbers using place value. • We will round numbers.

1 - 1 | Properties of Addition and Subtraction Solve. DAILY REV IE W

4+5=

9−5=

7+3=

10 − 2 =

L E A R N A ND C ONNEC T Addition and subtraction rules can help us find the sum or difference. Numbers can be added in any order.

3+5=8

5+3=8

8+0=8

Numbers cannot be subtracted in any order. 10 − 3 = 7

Adding or subtracting zero does not change the number. 8−0=8

Subtracting a number from itself leaves zero.

3 − 10 ≠ 7

8−8=0

AP P LY Fill in the blanks to make the number sentence true. 1. 4. 7.

+ 12

6+8=8+

+ 10 = 10 + 7

63 +

12 − 0 =

12 + 5 =

15 + 0 =

10. 11 − 0 =

= 5 + 63

11. 8 + 0 =

Commutative property of addition - numbers can be added in any order Associative property of addition - when adding, numbers can be grouped in different ways Identity property - adding or subtracting zero doesn’t change the value of a number

Level E

| Chapter 1 - 1

14 + 4 =

3+8=8+

0 + 24 =

12. 0 + 48 =

Vocabulary

| Lighthouse MATH

+ 14

Exercise | 1 - 1 Name

Solve. 1.

5 + 6

5 − 1

7 + 6

6 + 3

6 + 4

12 + 5

8 + 0

5 − 5

9 − 2

10.

4 + 6

11.

5 + 4

12.

11 + 4

13.

0 + 7

14.

13 − 0

15.

4 + 11

16.

1 + 2

17.

2 − 2

18.

10 + 5

19.

17 − 3

20.

6 + 0

21.

8 + 2

22.

0 + 7

23.

5 + 12

24.

8 + 11

25.

7 + 4

26.

2 + 8

27.

6 + 5

28.

9 + 0

29.

4 + 5

30.

2 + 6

Add. Group the numbers in any way. 32. 4 + 6 + 8 =

33. 11 + 1 + 8 =

Solve. 35. Joseph has 8 marbles. He does not lose any marbles in the game. How many marbles does he have?

34. Joseph has 3 red marbles and 5 yellow marbles. Andrew has 5 red marbles and 3 yellow marbles. Who has more marbles?

CH AL L ENGE Group the addends in a different way to find the missing number. 37. 10 + (5 + 2) =

36. (14 + 5) + 1 = 14 +

Level E

| Chapter 1 - 1

| Lighthouse MATH

31. 3 + 6 + 8 =

1 - 2 | Addition and Subtraction as Inverse Operations Solve. 1.

DAILY REV IE W

7 + 3

3 + 7

4 + 2

L E A R N A ND C ONNEC T

9 6

15 −

6 9

9 − 4

We can check subtraction with addition. Start with your answer. Add the number you subtracted. 15 − 7

If you get the number you started with, your answer is correct.

8 +

7 15

If you get the number you started with, your answer is correct.

AP P LY Check the answer with addition or subtraction. Circle correct or incorrect. 1.

4 + 5 9

9 − 5

15 − 8 8

8 + 8

3 + 13 15

−

Correct

Incorrect

Correct

Incorrect

Correct Incorrect

10 − 8 3

3 + 8

4 + 8 12

12 − 8

11 − 5 6

Vocabulary Inverse operations - opposite operations such as addition and subtraction

Level E

| Chapter 1 - 2

8 − 0

1+2=3 3−2=1

Addition and subtraction are opposites. We can check addition with subtraction. Start with your answer. Subtract the number you added.

2 + 4

| Lighthouse MATH

Correct Incorrect

Exercise | 1 - 2 Name

Add. Then, check your answer using subtraction. 1.

8 + 9

7 + 6

−

3 + 7

−

10 + 1

4 + 5

−

10.

1 + 4

−

2 + 3

12 + 2

−

11.

2 + 8

−

6 + 9

−

8 + 3

−

12.

4 + 9

−

16.

15 − 8

20.

18 − 7

24.

13 − 3

13.

16 − 8

17.

7 − 6

21.

10 − 6

14.

11 − 4

18.

14 − 5

22.

12 − 9

15.

12 − 4

19.

14 − 7

23.

7 − 5

Subtract. Then, check your answer using addition.

Solve. 25. Danny has 18 candies. He gives away 6 of them. How many does he have left?

26. Pete has $5. He gets $4 more for mowing the lawn. How much money does he have in total?

CH AL L ENGE Fill in the blanks. 27. 8 +

= 10

28. 3 +

Level E

| Chapter 1 - 2

| Lighthouse MATH

29. 14 −

1 - 3 | Addition and Subtraction Fact Families Solve. 1.

DAILY REV IE W

7 + 2

3 + 10

9 − 4

18 − 6

5 + 6

10 − 6

L E A R N A ND C ONNEC T A fact family is a group of two addition facts and two subtraction facts with the same numbers.

6, 9, 15 6 + 9 = 15 9 + 6 = 15

6 + 9 = 15 9 + 6 = 15

15 − 9 = 6 15 − 6 = 9

AP P LY

Write the fact families for the following sets of numbers. 1.

1, 8, 9

2, 12, 14

3, 10, 7

4, 16, 12

2, 10, 12

2, 6, 8

5, 4, 9

16, 8, 8

10. 7, 8, 15

Level E

| Chapter 1 - 3

| Lighthouse MATH

19, 15, 4

Exercise | 1 - 3 Name

Write the fact families for the following sets of numbers. 1.

4, 8, 12

3, 13, 10

5, 11, 6

12, 12, 0

14, 3, 11

Solve. 6.

16 − 2

16 − 14

11 − 7

11 − 4

10.

12 − 9

11.

12 − 3

12.

3 + 7

13.

7 + 3

14.

3 + 1

15.

1 + 3

16.

5 + 9

17.

9 + 5

18. 8 + 5 =

19. 5 + 8 =

20. 1 + 0 =

21. 0 + 1 =

22. 16 − 9 =

23. 16 − 7 =

24. 9 − 9 =

25. 9 − 0 =

27. A grocery store has 12 bunches of bananas and sells 4 of them. How many are left?

26. There are 5 chocolate chip cookies and 10 sugar cookies on a plate in a bakery. How many cookies are there in all?

If an employee puts 4 more bunches on the shelf, how many will there be now?

If somebody buys 10 cookies, how many will be left?

CH AL L ENGE 28. When does a fact family have just two number sentences? Give examples to prove your answer.

Level E

| Chapter 1 - 3

| Lighthouse MATH

Solve.

1 - 4 | Place Value to the Thousands Place Add. 1.

DAILY REV IE W

10 + 2

10 + 7

10 + 3

10 + 5

10 + 6

L E A R N A ND C ONNEC T Digits are the numbers 0 - 9. Some numbers have 1 digit, and some have many digits. 3,692 has 4 digits. We can put each digit in a place value chart.

Thousands

We say, “three thousand, six hundred ninety-two”. We can write the expanded form by adding the values of each digit.

Hundreds

Tens

Ones

three thousand

six hundred

ninety

two

3,000

600

AP P LY Write the value of the underlined digit. 1. 1,564

2. 2,341

3. 1,692

4. 5,036

5. 7,325

6. 6,839

7. 8,341

8. 7,498

9. 8,417

10. 3,872

11. 5,128

12. 2,006

Level E

| Chapter 1 - 4

| Lighthouse MATH

Exercise | 1 - 4 Name

Write the number in expanded form. 1.

9,542

3,059

2,698

1,735

8,221

7,403

8,025

2,487

Write the number. 9. Eight thousand, nine hundred eighty-two

10. Nine thousand, eight hundred thirty-one

11. Six thousand, four hundred seven

12. Four thousand, thirty-five

13. Five thousand, two hundred eleven

14. Three thousand, four hundred twenty-eight

15. Two thousand, eight hundred fifty-nine

16. One thousand, two hundred forty-five

17. 4,935

18. 3,201

19. 9,356

20. 3,712

21. 4,002

22. 5,214

23. 6,427

24. 1,672

25. 5,398

26. 6,055

Write the value of the underlined digit.

CH AL L ENGE Solve. 27. Find a number that fits the following rules: The tens place is three more than the ones place. The hundreds place is four times the ones place. The thousands place is one less than the ones place. The ones place is a 2.

Level E

| Chapter 1 - 4

| Lighthouse MATH

1 - 5 | Place Value to the Billions Place Write the value of the underlined digit. 1. 4,471

DAILY REV IE W

2. 3,604

3. 3,658

4. 6,457

L E A R N A ND C ONNEC T The number 5,836,891,418 has 10 digits, so it is in the billions. We always put a comma after the billions, millions, and thousands places. Billions

Millions

Billions

Thousands

Hundred millions

Ten millions

Millions

Ones

Hundred Ten Thousands Hundreds thousands thousands

Tens

Ones

five billion, eight hundred thirty-six million, eight hundred ninety-one thousand, four hundred eighteen The digit 3 is in the ten millions place. It has a value of 30,000,000.

The digit 5 is in the billions place. It has a value of 5,000,000,000.

AP P LY Find the digit. 1. 4,985,671,024

Which digit is in the millions place?

2. 2,381,374,610

Which digit is in the thousands place?

3. 5,315,247,921

Which digit is in the ten thousands place?

4. 1,973,202,654

Which digit is in the billions place?

5. 3,751,008,432

Which digit is in the hundred millions place?

6. 8,095,428,356

Which digit is in the ten millions place?

Level E

| Chapter 1 - 5

| Lighthouse MATH

Exercise | 1 - 5 Name

Write the number. 1. Four billion, five hundred seventy-six million, eight hundred eighty-four thousand, five hundred twenty-seven

2. Five billion, three hundred five million, forty-four thousand, two hundred seventy-one

3. Seven billion, eight hundred fifty million, three hundred five thousand, two hundred fifty

4. Six billion, forty-one million, forty-five thousand, four hundred twenty-three

5. Five billion, seven hundred ninetyeight million, four hundred sixty-seven thousand, one hundred twelve

6. Seven hundred three million, four hundred two thousand, eight hundred eleven

7. 117,328,510

8. 81,921,042

9. 6,513,231

10. 7,948,082

11. 2,048,132,871

12. 7,628,119,632

13. 4,776,453,212

14. 5,312,543,978

15. 1,534,665,231

16. 4,212,315,678

17. 6,683,442,261

18. 1,115,738,903

Write the value of the underlined digit.

CH AL L ENGE Solve. 19. In which number does the digit 7 have a greater value: 4,675,352 or 4,768,356?

Level E

| Chapter 1 - 5

20. Which number has the greater value for the digit 2: 5,278,894 or 7,021,678?

| Lighthouse MATH

1 - 6 | Comparing and Ordering Numbers Subtract. DAILY REV IE W

12 − 5 =

16 − 8 =

11 − 9 =

2−0=

L E A R N A ND C ONNEC T A school district orders pencils for its schools. Order A has 265,000 pencils. Order B has 256,000 pencils. Which order has more pencils? To find which has more, compare the numbers.

Write > for greater than. Write < for less than.

Line up the numbers by place value.

First compare the numbers in the highest place value.

If needed, move to the right until you find digits that are different and compare them.

265,000 256,000

2=2

6>5

Since 265,000 > 256,000, Order A has more pencils.

We can write the numbers in order from least to greatest: 256,000; 265,000

AP P LY Write < or > in the circle. 1. 72

2. 375

4. 7,615

374

5. 8,564

7,515

9,453

3. 1,302

1,320

6. 10,015

10,105

Write the numbers in order from least to greatest. 7. 210

120 ,

8. 3,856

121 ,

Level E

3,568

4,658

| Chapter 1 - 6

| Lighthouse MATH

9. 12,112

12,212 ,

12,121 ,

Exercise | 1 - 6 Name

Write < or > in the circle. 1. 99

657

658

332

323

230

203

140

104

1,243

5,102

11. 3,128

3,218

12. 4,442

10. 5,112

1,233

13. 52,833

14. 10,006

52,822

15. 1,693,482

8,008

16. 304,672,009

1,691,482

5,442

340,618,010

Write the numbers in order from least to greatest. 17. 598

20. 2,187

498

18. 917

489

2,817

2,718

23. 200,115

200,015 ,

179

21. 1,321

19. 402

719

1,331

1,313

204

5,341

3,415

22. 1,534

24. 36,521,480

200,415

420

36,522,480

36,520,480

River

Length in Miles

Arkansas

1,469

Columbia

1,240

Mississippi

2,340

Missouri

2,540

Rio Grande

1,900

CH AL L ENGE Use the chart to answer the questions. 25. Which river is the longest? 26. Which river is the shortest? 27. How many rivers are longer than the Rio Grande? 28. List the rivers from longest to shortest. ,

Level E

| Chapter 1 - 6

| Lighthouse MATH

1 - 7 | Rounding Whole Numbers Compare the numbers using < or >. DAILY REV IE W

2. 32

L E A R N A ND C ONNEC T Mount Everest is the tallest mountain in the world. It is 29,032 feet tall. About how tall is it? Round 29,032 to the nearest thousand.

Mark the place you are rounding.

Look to the right of that digit.

Use the rules for rounding.

29,032

4 or lower: Marked number stays the same 5 or higher: Marked number goes up

29,032

Change the rest of the digits to zero. 29,000

AP P LY Round to the nearest hundred. 1. 798

2. 507

3. 655

4. 415

5. 323

6. 465

10. 2,760

11. 4,616

12. 7,081

16. 368

17. 6,299

18. 27

Round to the nearest thousand. 7. 8,536

8. 1,254

9. 6,792

Round to the highest place value. 13. 84

14. 729

15. 8,899

Level E

| Chapter 1 - 7

| Lighthouse MATH

Exercise | 1 - 7 Name

Round to the nearest hundred. 1. 728

2. 395

3. 769

4. 350

5. 572

6. 938

7. 8,318

8. 6,656

9. 6,966

10. 17,974

11. 30,672

12. 48,552

Round to the nearest thousand. 13. 1,871

14. 7,598

15. 6,587

16. 1,303

17. 9,580

18. 8,351

19. 28,532

20. 77,428

21. 64,072

22. 971,428

23. 33,560

24. 111,826

25. 67

26. 92

27. 621

28. 1,562

29. 8,923

30. 561,929

31. 301,942

32. 854,201

33. 4,982,306

34. 3,928,542

35. 42,335,141

36. 64,005,802

37. 38,419,625

38. 871,054,188

39. 366,234,805

CH AL L ENGE Solve. 40. A number rounds to 1,800 when rounded to the nearest hundred. It contains no zeros. What are the smallest and largest possible numbers it could be?

Level E

| Chapter 1 - 7

| Lighthouse MATH

Round to the highest place value.

1 - 8 | Chapter Review Round each number to the nearest thousand. 2. 9,491

1. 36,542

DAILY REV IE W

3. 632,287

4. 1,513,094

5. 3,427,499

L E T ' S REV I EW Addition and Subtraction Are Inverse Operations

Fact Families A group of 2 addition facts and 2 subtraction facts that all contain the same three numbers.

Check addition by subtracting. Check subtraction by adding. 18 + 5 = 23

3, 5, 8 3+5=8 8−5=3

23 − 5 = 18

Writing Numbers

Rounding Numbers

Standard form:

8,307

Expanded form:

8,000 + 300 + 7

Mark a place and look at the digit on its right. Use rounding rules to decide how to round. Round 6,752 to the nearest hundred:

Word form: Eight thousand, three hundred seven © Lighthouse Curriculum. Copying strictly prohibited.

5+3=8 8−3=5

6,752 rounds to 6,800

AP P LY Write the fact families for the following sets of numbers. 1. 3, 6, 9

2. 5, 2, 7

Level E

3. 4, 6, 10

| Chapter 1 - 8

4. 9, 2, 7

| Lighthouse MATH

5. 4, 8, 12

Exercise | 1 - 8 Name

Add. Then, check your answer using subtraction. 1.

6 + 9

−

4 + 7

−

8 + 1

−

7 + 6

−

8 − 4

Subtract. Then, check your answer using addition. 5.

8 − 2

7 − 4

9 − 4

Write in standard form. 9.

nineteen thousand, three hundred eighty

10. four million, two hundred five thousand, six hundred thirty-eight 11. eight million, twelve thousand Write in expanded form. 12. 19,380 =

13. 4,205,638 =

+ +

14. 732

15. 3,428

16. 1,876

17. 42,812

Round to the highest place value. 18. 910,402

Write < or > in the circle. 19. 4,213

20. 8,922

4,233

21. 13,284

8,902

13,283

Write the numbers in order from least to greatest. 22. 8,723

8,633 ,

23. 1,428,092

8,893

1,428,192

Level E

| Chapter 1 - 8

| Lighthouse MATH

1,427,092 ,

1 - 9 | Cumulative Review

Solve. 1.

8 + 5

6 + 9

4 + 7

13 − 4

10 − 3

17 − 8

4 − 2

4 + 9

7 + 1

10.

7 + 4

11.

2 − 1

12.

4 + 5

13.

5 − 4

14.

7 − 2

15.

8 + 1

16.

11 − 9

17.

7 + 9

18.

8 − 7

19.

7 − 3

20.

5 − 2

21.

4 + 8

22.

18 − 9

23.

3 + 7

24.

6 + 3

25.

2 + 6

26.

7 − 6

27.

6 − 5

28.

5 + 9

29.

10 − 8

30.

5 + 4

31.

13 − 5

32.

14 − 7

33.

11 − 3

34.

1 + 8

35.

16 − 9

36.

7 + 6

37.

14 − 9

38.

6 + 2

39.

14 − 6

40.

1 + 5

41.

10 − 7

42.

8 − 1

43.

4 − 1

44.

9 + 5

45.

10 − 2

46.

15 − 8

47.

12 − 3

48.

8 + 6

49.

4 + 3

50.

4 + 4

51.

9 − 3

52.

2 + 8

53.

13 − 6

54.

9 − 1

55.

9 − 5

56.

3 − 1

57.

11 − 2

58.

5 + 3

59.

6 + 8

60.

7 + 7

61.

3 + 3

62.

6 + 4

63.

15 − 6

64.

6 − 3

65.

14 − 8

66.

5 + 6

Level E

| Chapter 1 - 9

| Lighthouse MATH

Exercise | 1 - 9 Name

Add. 1.

5 + 6

4 + 2

8 + 9

2 + 6

2 + 2

8 + 3

4 + 9

6 + 2

8 + 7

10.

2 + 8

11.

9 + 5

12.

8 + 2

13.

5 + 1

14.

9 + 4

15.

5 + 8

16.

1 + 2

17.

3 + 4

18.

7 + 1

19.

8 − 7

20.

5 − 2

21.

11 − 8

22.

3 − 2

23.

5 − 1

24.

9 − 6

25.

7 − 6

26.

9 − 5

27.

10 − 8

28.

5 − 3

29.

12 − 5

30.

8 − 2

31.

12 − 9

32.

15 − 9

33.

14 − 6

34.

7 − 5

35.

13 − 8

36.

13 − 5 © Lighthouse Curriculum. Copying strictly prohibited.

Subtract.

Add. Then, check your answer using subtraction. 37.

7 + 4

−

38.

12 + 3

−

39.

4 + 5

−

40.

3 + 7

−

44.

11 − 5

Subtract. Then, check your answer using addition. 41.

10 − 4

42.

15 − 9

Level E

| Chapter 1 - 9

43.

14 − 8

| Lighthouse MATH

2 C H A P T E R

In Chapter 2, we will practice

Addition and Subtraction In this chapter, we will be adding and subtracting multi-digit numbers. When working with large numbers, it is important to keep your work organized. • We will add and subtract numbers by lining up their place values and working from right to left. • We will regroup when the sum in any place is greater than 9. • We will regroup when we need to subtract a larger digit from a smaller digit. • We will estimate sums and differences by rounding to easier numbers.

2 - 1 | Adding Two- and Three-Digit Numbers Add. 1.

DAILY REV IE W

22 + 9

58 + 6

96 + 3

26 + 4

36 + 5

16 + 9

L E A R N A ND C ONNEC T The Statue of Liberty stands on a base that is 154 feet tall. The statue is 151 feet tall. What is the total height of the statue and the base? To find the total height, add and . Line up the place values.

Add the ones. Regroup if needed.

151 + 154

Add the tens. Regroup if needed.

Add the hundreds. Regroup if needed.

151 + 154 5

151 + 154 305

151 + 154 05

The total height is 305 feet.

AP P LY Add. Regroup if needed. 1.

2. 1 2 1 + 4 6

3. 2 3 9 + 4 3

4. 4 6 3 + 8 8

Vocabulary Regrouping - when adding and getting a sum greater than 9, numbers are rewritten according to their place value

Level E

| Chapter 2 - 1

| Lighthouse MATH

5 7 7 + 1 5 2

Exercise | 2 - 1 Name

Add. 1.

543 + 26

340 + 236

618 + 203

419 + 81

326 + 78

808 + 166

255 + 98

639 + 260

117 + 67

10.

709 + 184

11.

391 + 45

12.

578 + 323

13.

772 + 204

14.

574 + 91

15.

266 + 226

16.

494 + 398

17.

922 + 19

18.

379 + 207

Rewrite and add. 19. 228 + 59

20. 23 + 670

21. 403 + 96

22. 297 + 138

23. 376 + 38

24. 590 + 326

25. 707 + 74

26. 621 + 182

27. Larry sold 119 cookies at the bake sale. Bob sold 97 cookies at the bake sale. How many total cookies did they sell?

Read the problem. Then solve. 28. Emma built a tower using 345 blocks. Kelly built a tower using 509 blocks. How many total blocks did they use?

CH AL L ENGE Fill in the blanks.

29. + 6 3

7 7 0

Level E

| Chapter 2 - 1

| Lighthouse MATH

2 - 2 | Adding Large Numbers Solve. DAILY REV IE W

372 + 68 =

13 + 709 =

268 + 73 =

182 + 664 =

L E A R N A ND C ONNEC T Ben walked 1,496 steps in the morning and 2,075 steps in the afternoon. How many steps did he walk altogether? To find the total number of steps, add . Add the ones. Regroup if needed.

and

Add the tens. Regroup if needed.

Add the hundreds. Regroup if needed.

1,496 + 2,075 1

Add the thousands. Regroup if needed.

1,496 + 2,075 71

1 1

1,496 + 2,075 3,571

1,496 + 2,075 571

Ben walked 3,571 steps in all.

AP P LY Add. 1.

2. 1 , 2 3 7 + 5 8 6

4 , 4 0 5 + 2 , 2 7 5

1 1 , 5 8 5 + 8 , 2 3 1

4 3 1 , 2 6 4 + 3 7 , 6 9 2

2 7 7 , 8 1 6 + 8 2 , 4 2 8

5 8 2 , 9 1 4 + 3 0 9 , 8 1 2

Level E

| Chapter 2 - 2

| Lighthouse MATH

Exercise | 2 - 2 Name

Add. 1.

2,343 + 1,026

7,240 + 2,196

25,508 + 12,962

16,347 + 6,903

44,069 + 17,284

549,373 + 3,826

73,040 + 1,296

95,471 + 3,956

2,917 + 1,203

10.

400,157 + 29,164

11.

8,338 + 3,137

12.

501,372 + 236,083

13.

207,135 + 39,608

14.

64,150 + 2,998

15.

4,419 + 3,005

Rewrite and add. 16. 42,282 + 3,967

17. 3,005 + 9,949

18. 74,043 + 9,619

19. 234,716 + 51,847

20. 60,503 + 38,601

21. 5,674 + 20,878

23. A factory makes 11,131 dolls and 351,096 balls. How many dolls and balls does it make in total?

22. Andrew read 1,385 pages of the book. Jeffrey read 2,086 pages. How many pages did they read altogether?

CH AL L ENGE Solve. 24. On Monday, the rubber duck factory makes 1,200 rubber ducks. Each day, it makes 250 more ducks than the day before. How many total rubber ducks will it make by the end of Friday?

Level E

| Chapter 2 - 2

| Lighthouse MATH

Read the problem. Then solve.

2 - 3 | Subtracting Two- and Three-Digit Numbers Solve. 1.

DAILY REV IE W

772 + 119

2,096 + 493

6,682 + 4,537

630,435 + 14,882

L E A R N A ND C ONNEC T A farmer needs 185 potatoes to sell at the market. So far, he has picked 46 potatoes. How many more potatoes does he need? To find how many more, subtract from .

Subtract the ones. Regroup if needed.

Line up the place values.

185 − 46

Subtract the tens. Regroup if needed.

Subtract the hundreds.

7 15

185 − 46 9

185 − 46 39

185 − 46 139

The farmer needs to pick 139 more potatoes.

AP P LY Subtract. 1.

2. 5 6 − 2 2

3. 6 4 − 3 9

Level E

4. 3 1 − 1 6

| Chapter 2 - 3

5. 1 8 4 − 7 4

| Lighthouse MATH

3 2 8 − 1 5 5

Exercise | 2 - 3 Name

Subtract. 1.

56 − 32

98 − 25

41 − 12

55 − 48

76 − 63

84 − 66

39 − 19

28 − 9

49 − 22

10.

63 − 35

11.

91 − 52

12.

70 − 35

13.

243 − 32

14.

171 − 68

15.

308 − 84

16.

590 − 77

17.

459 − 52

18.

632 − 99

Rewrite and subtract. 19. 248 − 167

20. 88 − 19

21. 404 − 292

22. 517 − 143

23. 118 − 63

24. 329 − 107

25. 574 − 398

26. 930 − 651

27. A zoo has 245 animals. 97 of them are large, and the rest are small. How many small animals are there?

Read the problem. Then solve. 28. Sara has 128 math problems to solve. She has finished 59 problems. How many more does she have left?

CH AL L ENGE Fill in the blanks.

9 1

29. −

9 1 8 5

Level E

| Chapter 2 - 3

| Lighthouse MATH

2 - 4 | Subtracting Across Zeros Subtract. 1.

DAILY REV IE W

84 − 55

128 − 71

218 − 147

435 − 262

793 − 379

L E A R N A ND C ONNEC T A toy store had 3,000 toys on its shelves. During a sale, 173 of them were sold. How many toys are left on the shelves? To find how many are left, subtract from .

Line up the place values.

Subtract the ones. Regroup one place value at a time.

3,000 − 173

99 2 10 10 10

Subtract the tens.

Subtract the hundreds.

99 2 10 10 10

3,000 − 173 7

3,000 − 173 27

Subtract the thousands.

99 2 10 10 10

3,000 − 173 827

3,000 − 173 2,827

There are 2,827 toys left.

AP P LY Subtract. 1.

2. 6 0 0 − 2 5 1

3. 8 0 0 − 2 3 2

Level E

| Chapter 2 - 4

4. 4 0 0 − 2 6 5

| Lighthouse MATH

9 0 0 − 3 3 0

Exercise | 2 - 4 Name

Subtract. 1.

500 − 192

600 − 162

700 − 264

8,000 − 426

9,000 − 689

5,010 − 538

4,500 − 443

2,800 − 628

4,405 − 759

10.

3,660 − 2,040

11.

5,007 − 2,879

12.

8,600 − 3,961

13.

6,500 − 2,676

14.

9,020 − 4,157

15.

8,008 − 6,320

Rewrite and subtract. 16. 3,200 − 1,189

17. 7,050 − 5,343

18. 8,003 − 4,638

19. 3,000 − 2,640

20. 6,020 − 4,324

21. 9,080 − 5,789

22. Mrs. Miller wants to bake 1,020 cookies for all the students and teachers at school. So far, she has baked 671 cookies. How many more cookies does she need to bake?

23. Leo wants to count 800 seeds inside of his giant pumpkin. He has counted 314 seeds. How many more seeds does he need to count?

CH AL L ENGE Solve. 24. 50,060 people lived in a town. One year, 2,164 people moved away. The next year, 4,098 people moved away. How many people live there now?

Level E

| Chapter 2 - 4

| Lighthouse MATH

Read the problem. Then solve.

2 - 5 | Subtracting Large Numbers Solve. 1.

DAILY REV IE W

3,700 − 548

8,020 − 4,199

1,004 − 386

6,450 − 2,505

L E A R N A ND C ONNEC T An airplane flew 272,946 miles last year. So far this year, it flew 24,901 miles. How many more miles did it fly last year than this year? To find the difference in the distances, subtract from . Line up the place values.

Subtract the ones.

Subtract one place value at a time, moving from right to left. Regroup if needed.

272,946 − 24,901

272,946 − 24,901 5

272,946 − 24,901 45

272,946 − 24,901 045

6 12

272,946 − 24,901 8,045

6 12

272,946 − 24,901 48,045

6 12

272,946 − 24,901 248,045

The airplane flew 248,045 more miles last year.

AP P LY Subtract. 1.

2. 1 5 2, 1 6 5 − 2 1, 3 4 1

2 0 6, 1 8 0 − 8 9, 7 0 8

5. 6 1 2, 0 6 2 − 5 7 2, 3 5 3

6. 5 0 0, 4 5 2 − 2 7 5, 2 5 7

Level E

3 9 1, 6 2 8 − 1 4, 0 6 7

| Chapter 2 - 5

| Lighthouse MATH

2 9 2, 8 6 4 − 2 0 9, 3 4 1

Exercise | 2 - 5 Name

Subtract. 1.

17,459 − 9,675

86,247 − 39,186

72,054 − 19,680

139,650 − 46,776

425,000 − 86,293

638,536 − 59,748

370,746 − 186,929

623,005 − 217,638

825,647 − 195,267

10.

506,000 − 163,667

11.

998,258 − 439,475

12.

608,250 − 129,186

Rewrite and subtract. 13. 37,651 − 12,975

14. 820,575 − 297,739

15. 126,359 − 75,278

16. 905,709 − 506,575

17. 325,026 − 178,675

18. 933,247 − 161,983

19. A car dealership sold 413,625 trucks in 2009. It sold 723,479 trucks in 2019. How many more trucks did it sell in 2019?

Read the problem. Then solve. 20. The Georgia Aquarium had 376,325 visitors in July and 196,377 visitors in December. How many more visitors came in July than in December?

CH AL L ENGE Solve. 21. Two six-digit numbers have a difference of 132,645. Neither number has any zeros in it. What could the two numbers be?

Level E

| Chapter 2 - 5

| Lighthouse MATH

2 - 6 | Estimating Sums and Differences Solve. 1.

DAILY REV IE W

27,006 − 11,887

190,091 − 45,252

618,510 − 315,826

L E A R N A ND C ONNEC T Ben’s Bakery needs to sell 1,964 cakes this month. In the past week, it sold 484 cakes. About how many more cakes does it need to sell? We don’t need to find the exact answer. To estimate the number of cakes, round and to their highest place value and subtract. Round the 1st number.

Round the 2nd number.

1,964 − 484

2,000

Subtract.

2,000 500

1,964 − 484

2,000 − 500 1,500

Ben's Bakery needs to sell about 1,500 more cakes.

AP P LY Round to the highest place value, then solve. 1.

921 − 384

3,421 + 1,899

−

6,782 + 2,130

124,500 − 76,200

Level E

| Chapter 2 - 6

−

| Lighthouse MATH

45,782 − 18,654

−

8,888 + 4,112

Exercise | 2 - 6 Name

Tip!

Round to the nearest ten to estimate the answer. 1.

52 + 28

67 − 12

−

161 + 34

When the digit to the right is… …4 or less, round down. …5 or more, round up.

Round to the nearest hundred to estimate the answer. 4.

709 − 227

7,716 − 5,370

−

419 + 497

6,120 + 2,784

359 − 161

−

9,234 − 140

−

12.

3,321 − 1,500

−

Round to the nearest thousand to estimate the answer. 10.

7,609 − 2,308

−

11.

5,050 + 1,925

Read the problem. Round to estimate the answer. © Lighthouse Curriculum. Copying strictly prohibited.

14. Anna’s Ice Pops usually sells 894 ice pops each week. This week, they only sold 519. About how many fewer ice pops did they sell this week?

13. Jeff takes a flight with two parts. The first part is 2,469 miles. The second part is 3,470 miles. About how many miles is the whole flight?

CH AL L ENGE Use rounding to solve. 15. Round 2,450 and 1,927 to the nearest hundred and subtract. Then, round each number to the nearest thousand and subtract. Which one is a better estimate?

Level E

| Chapter 2 - 6

| Lighthouse MATH

2 - 7 | Chapter Review Round each number to its highest place value to estimate the sum. 1.

DAILY REV IE W

4,521 + 308

12,918 + 3,562

568 + 491

L E T ' S REV I EW Adding Large Numbers

Subtracting Large Numbers

Line up the place values. Add straight down, starting from the ones and moving left. Regroup if needed.

Line up the place values. Subtract straight down, starting from the ones and moving left. Regroup if needed. 12 11 11 0 2 1 1 13

1 1 1

4,937 + 8,286 13,223

13,223 − 8,286 4,937

Rounding to Estimate Sums and Differences

9,128 + 3,672

9,000 4,000 13,000

6,782 − 2,130

−

7,000 2,000 5,000

AP P LY Add. 1.

744,282 + 166,460

964,481 + 867,689

724,046 + 488,139

908,478 + 841,787

739,857 + 142,507

337,223 + 105,471

408,074 + 303,683

878,024 + 697,976

599,605 + 15,432

10.

971,135 + 390,665

Level E

| Chapter 2 - 7

| Lighthouse MATH

Exercise | 2 - 7 Name

Subtract. 1.

268,897 − 63,125

555,598 − 155,291

27,539 − 22,212

156,866 − 140,232

242,884 − 12,860

15,006 − 12,866

765,726 − 212,835

100,910 − 8,518

338,191 − 35,911

10.

228,121 − 214,107

Round each number to the nearest hundred. Then add or subtract. 11.

593 − 131

−

14.

6,548 − 2,463

−

12.

293 + 431

15.

7,462 + 1,437

13.

5,431 − 2,218

−

16.

8,219 − 468

−

17.

4,638 + 4,642

20.

7,462 + 1,437

18.

3,427 + 3,418

21.

6,548 − 2,463

−

19.

5,431 − 2,618

−

22.

8,221 − 3,895

−

Round each number to the nearest thousand. Then add or subtract.

Round each number to the highest place value. Then add or subtract. 23.

724 − 198

26.

66,018 − 22,925

−

24.

2,894 + 3,972

27.

71,235 + 5,923

Level E

| Chapter 2 - 7

| Lighthouse MATH

12,523 − 4,110

−

28.

24,893 − 10,375

−

2 - 8 | Cumulative Review

Solve. 1.

15 − 8

1 + 4

11 − 2

3 + 5

2 − 1

11 − 4

3 + 7

1 + 7

9 + 5

10.

3 + 8

11.

14 − 8

12.

12 − 7

13.

6 + 6

14.

9 − 3

15.

3 + 4

16.

9 − 4

17.

4 + 4

18.

6 − 4

19.

12 − 3

20.

8 + 6

21.

4 + 3

22.

11 − 5

23.

5 − 3

24.

16 − 7

25.

6 + 2

26.

10 − 8

27.

15 − 7

28.

16 − 8

29.

11 − 7

30.

6 + 5

31.

8 + 2

32.

7 + 6

33.

10 − 6

34.

7 + 3

35.

8 + 7

36.

7 + 4

37.

2 + 3

38.

10 − 3

39.

5 + 1

40.

7 − 2

41.

4 + 5

42.

8 + 5

43.

5 + 5

44.

8 + 1

45.

9 + 8

46.

4 − 1

47.

3 + 6

48.

9 − 1

49.

10 − 5

50.

8 − 5

51.

3 + 2

52.

8 − 3

53.

9 + 4

54.

6 − 5

55.

11 − 6

56.

14 − 6

57.

7 + 1

58.

9 + 2

59.

5 + 9

60.

10 − 1

61.

1 + 2

62.

8 + 4

63.

13 − 5

64.

4 + 2

65.

6 + 8

66.

11 − 3

Level E

| Chapter 2 - 8

| Lighthouse MATH

Exercise | 2 - 8 Name

Add. 1.

861 + 675

442 + 120

189 + 368

543 + 640

938 + 662

6,431 + 4,283

4,113 + 7,635

2,121 + 5,094

3,028 + 4,671

10.

2,208 + 1,413

Subtract. 11.

601 − 268

12.

850 − 424

13.

813 − 323

14.

247 − 90

15.

931 − 365

16.

8,291 − 5,712

17.

8,938 − 1,781

18.

9,537 − 5,185

19.

3,692 − 2,392

20.

6,408 − 2,428

21. Eight thousand, three hundred fifty-three

22. Thirty-two thousand, five hundred six

23. Six hundred eighty-one thousand, nine hundred fifty-seven

24. Sixteen thousand, seven hundred eighteen

Write in standard form.

Write the value of the underlined digit. 25. 3,423,583

26. 16,392

27. 49,367,301

28. 116,741

29. 46,354,234,118

30. 1,345,232,962

31. 1,297,321,486

32. 4,502,348

Level E

| Chapter 2 - 8

| Lighthouse MATH

3 C H A P T E R

In Chapter 3, we will practice

Multiplication Facts Multiplication is repeated addition. When many equal groups are added together, we can find the total by multiplying. • We will practice multiplying by 0 through 12. • We will learn strategies to solve multiplication facts. • We will learn properties of multiplication that make solving easier.

3 - 1 | Multiplication Facts 2, 3, 4, and 5 Solve. 1. DAILY REV IE W

2 2 + 2

5 5 5 + 5

9 + 9

facts, you can try these tricks.

To multiply a number by 3, you can add it three times.

2×4 Double 4 is 8.

To multiply a number by 4, you can double it, then double it again.

4 4 4 4 + 4

If you forget one of the

L E A R N A ND C ONNEC T To multiply a number by 2, you can double it.

3×3 3+3+3=9

To multiply a number by 5, you can skip count by fives that number of times.

4×6 Double 6 is 12. Double 12 is 24.

5×5 5, 10, 15, 20, 25

AP P LY Solve. 1.

6 × 2

7 × 5

10 × 4

8 × 3

5 × 2

7 × 2

9 × 2

5 × 9

12 × 3

10.

4 × 7

11.

9 × 3

12.

4 × 5

13.

2 × 3

14.

5 × 5

15.

11 × 4

16.

3 × 7

17.

3 × 3

18.

4 × 4

Level E

| Chapter 3 - 1

| Lighthouse MATH

Exercise | 3 - 1 Name

8 × 2

1 × 4

12 × 3

5 × 6

7 × 4

9 × 2

5 × 3

12 × 5

8 × 5

10.

4 × 8

11.

4 × 9

12.

3 × 7

13.

6 × 4

14.

9 × 5

15.

7 × 5

16.

5 × 1

17.

3 × 5

18.

4 × 2

19.

3 × 4

20.

8 × 5

21.

4 × 9

22.

2 × 9

23.

4 × 6

24.

3 × 1

25.

2 × 12

26.

1 × 2

27.

3 × 12

28.

10 × 3

29.

4 × 12

30.

5 × 7

31.

12 × 4

32.

6 × 3

33.

10 × 4

34.

8 × 2

35.

11 × 3

36.

4 × 8

37.

5 × 4

38.

2 × 5

39.

2 × 7

40.

4 × 1

41.

2 × 1

42.

2 × 3

Multiply.

CH AL L ENGE Solve. 43. 2 × 2 × 2 =

44. 5 × 2 × 5 =

Level E

| Chapter 3 - 1

45. 3 × 2 × 3 =

| Lighthouse MATH

3 - 2 | Multiplication Facts 6, 7, 8, and 9 Solve. DAILY REV IE W

2×3=

5×4=

2×9=

If you forget one of the

facts, you can try these tricks.

L E A R N A ND C ONNEC T

To multiply a number by 6, you can multiply by three and then double it.

To multiply a number by 8, you can multiply by four and then double it.

3×8=

To multiply a number by 7, you can multiply by 6 and add one more group.

6×5 5 times 3 is 15. Double 15 is 30.

6 times 4 is 24. Double 24 is 48.

6 × 5 is 30. 30 plus 5 is 35.

To multiply a number by 9, you can use your hands.

8×6

7×5

9 10

9 × 4 = 36

AP P LY Solve. 1.

6 × 5

7 × 3

10 × 6

8 × 7

6 × 8

7 × 4

8 × 2

9 × 9

12 × 6

10.

7 × 7

11.

9 × 7

12.

4 × 8

13.

8 × 8

14.

6 × 9

15.

6 × 6

16.

6 × 7

17.

5 × 7

18.

10 × 8

Level E

| Chapter 3 - 2

| Lighthouse MATH

Exercise | 3 - 2 Name

9 × 2

1 × 8

6 × 4

9 × 6

8 × 4

10 × 9

6 × 3

11 × 6

6 × 5

10.

5 × 8

11.

3 × 9

12.

8 × 7

13.

9 × 4

14.

9 × 5

15.

7 × 7

16.

9 × 1

17.

8 × 8

18.

7 × 2

19.

3 × 8

20.

8 × 5

21.

4 × 9

22.

2 × 6

23.

4 × 6

24.

9 × 2

25.

7 × 12

26.

1 × 6

27.

3 × 7

28.

10 × 7

29.

8 × 12

30.

5 × 7

31.

11 × 8

32.

6 × 3

33.

10 × 9

34.

8 × 2

35.

11 × 7

36.

6 × 8

37.

6 × 5

38.

2 × 7

39.

8 × 1

40.

9 × 1

41.

8 × 8

42.

6 × 9

Multiply.

CH AL L ENGE Solve. 43. 6 × 4 × 2 =

44. 5 × 2 × 8 =

Level E

| Chapter 3 - 2

45. 7 × 2 × 2 =

| Lighthouse MATH

3 - 3 | Multiplication Facts 0, 1, and 10 Solve. DAILY REV IE W

6×4=

6×7=

9×8=

7×5=

If you forget one of the

facts, you can try these tricks.

L E A R N A ND C ONNEC T

A number multiplied by 0 is 0.

A number multiplied by 1 is that number.

To multiply by 10, write the number and add one zero at the end.

0 × 8 is 0.

8 × 1 is 8.

8 × 10 is 80.

AP P LY

Solve. 1.

6 × 0

1 × 5

10 × 4

1 × 3

0 × 8

7 × 10

9 × 1

1 × 0

10 × 3

10.

0 × 7

11.

1 × 1

12.

4 × 1

13.

2 × 1

14.

10 × 10

15.

1 × 5

16.

10 × 6

17.

9 × 0

18.

8 × 1

19.

1 × 7

20.

8 × 10

21.

9 × 1

22.

2 × 10

23.

9 × 10

24.

2 × 1

25.

0 × 11

26.

5 × 0

27.

6 × 1

28.

8 × 1

29.

1 × 7

30.

8 × 0

Level E

| Chapter 3 - 3

| Lighthouse MATH

Exercise | 3 - 3 Name

9 × 7

12 × 1

1 × 6

10 × 7

1 × 3

12 × 4

12 × 3

3 × 7

10 × 8

10.

4 × 8

11.

9 × 6

12.

4 × 2

13.

5 × 10

14.

2 × 2

15.

5 × 6

16.

9 × 10

17.

11 × 6

18.

11 × 1

19.

5 × 8

20.

9 × 4

21.

2 × 3

22.

5 × 3

23.

6 × 7

24.

0 × 10

25.

5 × 7

26.

3 × 4

27.

7 × 0

28.

8 × 8

29.

6 × 0

30.

11 × 5

31.

11 × 8

32.

7 × 2

33.

5 × 2

34.

4 × 6

35.

1 × 1

36.

0 × 1

37.

11 × 0

38.

3 × 6

39.

9 × 1

40.

4 × 1

41.

2 × 5

42.

8 × 4

Multiply.

CH AL L ENGE Solve. 43. 5 × 0 × 2 =

44. 5 × 2 × 0 =

Level E

| Chapter 3 - 3

45. 0 × 5 × 2 =

| Lighthouse MATH

3 - 4 | Multiplication Facts 11 and 12 Solve. DAILY REV IE W

0×4=

1×7=

8×1=

If you forget one of the

facts, you can try these tricks.

L E A R N A ND C ONNEC T

A single-digit number multiplied by 11 is that digit repeated.

Double-digit numbers multiplied by 11 can also be figured out this way.

To multiply a number by 12, you can multiply by 10 and then add double that number.

11 × 12

11 × 6 = 66

7 × 10 =

Write 1 ___ 2

Add 1 + 2 = 3

Put 3 in the middle → 132

3 × 12 3 × 10 = 30; double 3 is 6. 30 + 6 = 36

AP P LY

Solve. 1.

11 × 2

12 × 5

10 × 12

8 × 11

4 × 12

12 × 2

11 × 5

11 × 9

12 × 3

10.

11 × 7

11.

12 × 7

12.

4 × 11

13.

6 × 11

14.

12 × 6

15.

12 × 11

16.

11 × 10

17.

11 × 4

18.

9 × 11

19.

2 × 11

20.

1 × 11

21.

3 × 12

22.

1 × 12

23.

12 × 8

24.

5 × 12

Level E

| Chapter 3 - 4

| Lighthouse MATH

Exercise | 3 - 4 Name

12 × 10

6 × 9

4 × 4

12 × 11

2 × 1

6 × 7

9 × 10

3 × 11

3 × 3

10.

5 × 0

11.

9 × 2

12.

6 × 5

13.

4 × 8

14.

9 × 1

15.

7 × 12

16.

2 × 6

17.

3 × 10

18.

10 × 11

19.

11 × 12

20.

3 × 12

21.

12 × 6

22.

3 × 1

23.

6 × 1

24.

0 × 0

25.

5 × 3

26.

2 × 8

27.

3 × 0

28.

8 × 4

29.

2 × 2

30.

3 × 6

31.

2 × 4

32.

5 × 7

33.

1 × 2

34.

7 × 6

35.

8 × 3

36.

9 × 11

37.

2 × 5

38.

8 × 12

39.

2 × 0

40.

4 × 9

41.

11 × 1

42.

8 × 1

Multiply.

CH AL L ENGE Solve. 43. 5 × 0 × 2 =

44. 5 × 2 × 0 =

Level E

| Chapter 3 - 4

45. 0 × 5 × 2 =

| Lighthouse MATH

3 - 5 | Multiplication Properties Solve. DAILY REV IE W

12 × 5 =

11 × 2 =

11 × 10 =

4 × 12 =

L E A R N A ND C ONNEC T

Numbers can be multiplied in any order.

Any number multiplied by 1 equals itself.

3×2=6

2×3=6

5×1=5

1×3=3

2 rows of 3

3 rows of 2

1 row of 5

3 rows of 1

When multiplying three or more numbers, you can choose which numbers to multiply first. 6

2 × 3 × 5 = 30

0 multiplied by a number equals 0.

4×0=0

0×8=0

2 × 3 × 5 = 30

AP P LY Multiply in any order. 1.

7×4=

4×7=

8×3=

3×8=

5×4×2=

4×2×5=

2×4×5=

7×1=

10. 0 × 4 =

Level E

| Chapter 3 - 5

11. 1 × 6 =

| Lighthouse MATH

12. 9 × 0 =

Exercise | 3 - 5 Name

Multiply. 1.

8 × 2

2 × 8

0 × 5

1 × 2

8 × 9

9 × 8

10 × 1

12 × 0

0 × 0

10.

1 × 1

11.

1 × 0

12.

12 × 1

13.

3 × 7

14.

7 × 3

15.

2 × 10

16.

10 × 2

17.

6 × 2

18.

2 × 6

19.

7 × 4

20.

0 × 2

21.

6 × 1

22.

4 × 7

23.

3 × 1

24.

6 × 0

25. 8 × 2 × 1 =

26. 5 × 2 × 2 =

27. 4 × 3 × 2 =

28. 4 × 1 × 6 =

29. 7 × 2 × 0 =

30. 6 × 5 × 1 =

31. 4 × 5 × 3 =

32. 8 × 5 × 0 =

33. 9 × 3 × 1 =

34. 1 × 7 × 3 =

35. 10 × 1 × 7 =

36. 4 × 2 × 3 =

Multiply.

CH AL L ENGE Solve. 37. 12 × 11 × 2 =

38. 11 × 12 × 2 =

Level E

| Chapter 3 - 5

39. 10 × 10 × 9 =

| Lighthouse MATH

40. 9 × 10 × 10 =

3 - 6 | Chapter Review Solve. DAILY REV IE W

12 × 5 =

8×5=

11 × 10 =

7×4=

L E T ' S REV I EW Complete the times tables. 1.

2 Times Table

2×1 = 2×2 = 2×3 = 2×4 = 2×5 = 2×6 = 2×7 = 2×8 = 2×9 = 2 × 10 =

5 Times Table

8 Times Table

6 Times Table

9 Times Table 9×1 = 9×2 = 9×3 = 9×4 = 9×5 = 9×6 = 9×7 = 9×8 = 9×9 = 9 × 10 =

Level E

| Chapter 3 - 6

| Lighthouse MATH

4 Times Table 4×1 = 4×2 = 4×3 = 4×4 = 4×5 = 4×6 = 4×7 = 4×8 = 4×9 = 4 × 10 =

6×1 = 6×2 = 6×3 = 6×4 = 6×5 = 6×6 = 6×7 = 6×8 = 6×9 = 6 × 10 =

8×1 = 8×2 = 8×3 = 8×4 = 8×5 = 8×6 = 8×7 = 8×8 = 8×9 = 8 × 10 =

3×1 = 3×2 = 3×3 = 3×4 = 3×5 = 3×6 = 3×7 = 3×8 = 3×9 = 3 × 10 =

5×1 = 5×2 = 5×3 = 5×4 = 5×5 = 5×6 = 5×7 = 5×8 = 5×9 = 5 × 10 = 7.

3 Times Table

7 Times Table 7×1 = 7×2 = 7×3 = 7×4 = 7×5 = 7×6 = 7×7 = 7×8 = 7×9 = 7 × 10 =

12 Times Table 12 × 1 = 12 × 2 = 12 × 3 = 12 × 4 = 12 × 5 = 12 × 6 = 12 × 7 = 12 × 8 = 12 × 9 = 12 × 10 =

Exercise | 3 - 6 Name

1 × 11

9 × 8

4 × 8

3 × 1

4 × 11

2 × 6

5 × 7

6 × 8

9 × 3

10.

5 × 8

11.

9 × 11

12.

5 × 0

13.

5 × 6

14.

3 × 12

15.

7 × 10

16.

11 × 0

17.

10 × 12

18.

1 × 7

19.

12 × 9

20.

10 × 4

21.

3 × 7

22.

4 × 5

23.

6 × 2

24.

1 × 4

25.

0 × 0

26.

11 × 9

27.

8 × 10

28.

7 × 4

29.

3 × 6

30.

8 × 8

31.

6 × 3

32.

9 × 7

33.

0 × 10

34.

9 × 4

35.

5 × 11

36.

5 × 9

37.

1 × 2

38.

12 × 10

39.

11 × 11

40.

8 × 4

41.

0 × 1

42.

2 × 5

Multiply.

CH AL L ENGE Solve. 43. 4 × 11 × 2 =

44. 4 × 5 × 4 =

Level E

| Chapter 3 - 6

45. 8 × 10 × 0 =

| Lighthouse MATH

46. 11 × 1 × 5 =

3 - 7 | Cumulative Review

Solve. 1.

3 + 1

1 + 2

8 + 7

12 − 5

9 + 8

7 − 5

5 − 3

4 + 3

2 × 4

10.

4 × 3

11.

9 − 6

12.

7 + 6

13.

4 + 6

14.

7 × 8

15.

9 − 1

16.

5 + 5

17.

8 − 4

18.

11 − 9

19.

8 × 6

20.

10 − 6

21.

2 − 1

22.

14 − 6

23.

13 − 5

24.

6 − 4

25.

1 × 2

26.

11 − 7

27.

6 + 1

28.

6 + 4

29.

15 − 7

30.

13 − 7

31.

1 + 1

32.

3 + 7

33.

4 + 5

34.

8 + 8

35.

1 + 5

36.

2 + 7

37.

5 + 1

38.

2 + 2

39.

8 − 5

40.

8 − 1

41.

5 + 3

42.

8 − 2

43.

5 × 8

44.

4 − 2

45.

14 − 9

46.

2 × 9

47.

9 + 3

48.

2 × 3

49.

8 + 1

50.

7 × 6

51.

11 − 8

52.

10 − 3

53.

9 − 5

54.

1 + 4

55.

7 + 5

56.

7 − 2

57.

7 − 6

58.

14 − 7

59.

17 − 8

60.

5 + 7

61.

13 − 6

62.

6 + 5

63.

2 + 4

Level E

| Chapter 3 - 7

| Lighthouse MATH

Exercise | 3 - 7 Name

Add. 1.

626 + 353

597 + 201

122 + 277

5,521 + 8,385

5,807 + 1,953

9,771 + 1,285

173 − 77

548 − 32

10.

3,619 − 866

11.

4,647 − 1,369

12.

5,011 − 673

Subtract. 7.

716 − 355

Multiply. 6 × 6

14.

7 × 7

15.

8 × 6

16.

5 × 6

17.

3 × 9

18.

9 × 1

19.

4 × 6

20.

7 × 3

21.

6 × 0

22.

2 × 2

23.

8 × 3

24.

4 × 0

25.

2 × 7

26.

6 × 1

13.

Write the number in expanded form. 27. 6,832 = 28. 43,115 = 29. 824,564 = 30. 29,041 = 31. 13,080 = 32. 501,492 =

Level E

| Chapter 3 - 7

| Lighthouse MATH

4 C H A P T E R

In Chapter 4, we will practice

Multidigit Multiplication In this chapter, we will be multiplying by two- and three-digit numbers. When multiplying large numbers, it is important to keep your work organized. • We will multiply multiples of 10, 100, and 1,000. • We will multiply by one-digit numbers. • We will multiply by multiples of ten. • We will multiply by two-digit numbers. • We will multiply by three-digit numbers.

4 - 1 | Multiplying Multiples of 10, 100, and 1,000 Multiply. 1.

DAILY REV IE W

5 × 7

6 × 2

5 × 8

6 × 7

4 × 9

L E A R N A ND C ONNEC T There are 40 boxes of beads. Each box has 8,000 beads. How many beads are there in all? To find the total number of beads, multiply by .

Multiply the numbers before the zeros.

Count up the zeros from both numbers. Add that many zeros to the end of the answer.

40 × 8,000 = 32

40 × 8,000 = 320,000

There are 320,000 beads in all.

AP P LY Multiply. 1.

3×5=

6×2=

7×3=

3 × 50 =

6 × 20 =

70 × 3 =

3 × 500 =

60 × 20 =

700 × 3 =

3 × 5,000 =

60 × 200 =

700 × 30 =

30 × 5,000 =

600 × 200 =

700 × 300 =

300 × 5,000 =

600 × 2,000 =

700 × 3,000 =

Level E

| Chapter 4 - 1

| Lighthouse MATH

Exercise | 4 - 1 Name

Multiply. 1.

6,000 × 3

9,000 × 4

6,000 × 7

5,000 × 9

2,000 × 2

400 × 30

600 × 40

5,000 × 70

8,000 × 90

10.

4,000 × 20

11.

3,000 × 300

12.

6,000 × 300

13.

5,000 × 900

14.

7,000 × 2,000

15.

4,000 × 7,000

Multiply. 16. 30 × 20 =

17. 40 × 50 =

18. 60 × 20 =

19. 200 × 30 =

20. 700 × 60 =

21. 600 × 2,000 =

23. A set of building blocks comes with 400 pieces. How many pieces would 30 sets have?

22. A big sale lasted for 10 days. Each day, about 4,000 customers came to the store. How many customers came during the whole sale?

CH AL L ENGE Solve and explain. 24. Solve the problem 50 × 800. Why are there more zeros in the answer than there were in the original numbers?

Level E

| Chapter 4 - 1

| Lighthouse MATH

Read the problem. Then solve.

4 - 2 | Multiplying by a One-Digit Number Multiply. 1.

DAILY REV IE W

90 × 2

70 × 3

50 × 90

200 × 60

700 × 900

L E A R N A ND C ONNEC T An art set has 124 pieces. The class has 8 art sets. How many pieces are there in all? To find the number of pieces, multiply by . Multiply the ones. Regroup if needed.

Multiply the tens. Add the extra tens from regrouping.

Multiply the hundreds. Add the extra hundreds from regrouping.

124 × 8 2

124 × 8 992

124 × 8 92

There are 992 pieces in all.

AP P LY Multiply. 1.

2. 1 6 × 4

2 7 × 2

7. 1 6 3 × 3

4. 8 1 × 5

8. 2 5 2 × 6

Level E

5. 9 8 × 4

9. 8 5 5 × 4

| Chapter 4 - 2

3 0 × 4

10. 7 0 2 × 6

| Lighthouse MATH

4 5 7 × 2

Exercise | 4 - 2 Name

Multiply. 1.

52 × 5

13 × 6

94 × 2

63 × 9

25 × 6

276 × 8

264 × 2

452 × 3

753 × 6

10.

668 × 5

11.

1,452 × 4

12.

4,483 × 2

13.

6,301 × 5

14.

5,524 × 7

15.

3,052 × 3

Rewrite and multiply. 16. 532 × 8

17. 471 × 5

18. 4 × 807

19. 2 × 2,443

20. 5 × 6,244

21. 3,502 × 7

22. There are 241 cars in a parking lot. If each car has 4 tires, how many tires are there?

23. A town has 4,511 residents. The city wants to plant 2 flowers for each resident. How many flowers need to be planted?

CH AL L ENGE Find the missing digits to make the problems true. 24.

2 6 × 3 858

25.

3 5 × 4 1,460

Level E

| Chapter 4 - 2

26.

47 × 5 2,735

| Lighthouse MATH

27.

21 × 3 657

Read the problem. Then solve.

4 - 3 | Multiplying by Multiples of 10 Multiply. 1.

DAILY REV IE W

24 × 3

45 × 6

87 × 2

72 × 9

56 × 4

L E A R N A ND C ONNEC T A group of 40 students wants to go to an aquarium. Tickets are $13 each. What is the total cost of all the tickets? To find the total cost, multiply

Multiply by the ones digit.

Multiply by the tens digit.

When we multiply by 0, the answer is 0.

13 × 40 0

Tip! You can multiply the non-zero digits, then add on the zero.

13 × 40 20

13 40 520

13 × 40 520

13 40 52

The total cost is $520.

AP P LY Multiply. 1.

2. ×

1 8 3 0

0 6.

2 5 5 0

4. ×

0 7.

1 2 2 × 5 0

3. 3 7 2 0

Level E

0 8.

3 2 4 × 2 0

5. 9 4 7 0 0

9. 2 2 7 × 1 0

| Chapter 4 - 3

9 2 5 0 0

10. 2 4 5 × 2 0

| Lighthouse MATH

1 4 2 × 3 0

Exercise | 4 - 3 Name

Multiply. 1.

36 × 20

57 × 60

11 × 30

42 × 80

87 × 40

46 × 50

59 × 90

92 × 20

25 × 20

10.

63 × 50

Rewrite and multiply. 11. 72 × 80

12. 33 × 50

13. 54 × 70

14. 224 × 20

15. 65 × 40

16. 135 × 70

17. A florist shop sells bouquets of flowers for $16 each. If they sell 40 bouquets, how much do they make?

18. A baker wants to make 60 cupcakes. Each cupcake will have 12 candy pieces. How many candy pieces does the baker need?

CH AL L ENGE Look at the pattern and explain. 19. How is multiplying by multiples of 10 similar to multiplying by multiples of 100? How is it different?

Level E

| Chapter 4 - 3

16 × 2 = 32 16 × 20 = 320 16 × 200 = 3,200

| Lighthouse MATH

43 × 3 = 129 43 × 30 = 1,290 43 × 300 = 12,900

Read the problem. Then solve.

4 - 4 | Multiplying by a Two-Digit Number Multiply. 1.

DAILY REV IE W

21 × 30

39 × 50

87 × 20

47 × 80

55 × 40

L E A R N A ND C ONNEC T A book has 224 pages. A printer prints 16 copies of the book. How many pages are printed? To find the total, multiply

Multiply by the ones digit.

Add a zero. Erase any numbers you carried.

224 × 16 4

224 × 16 44

224 × 16 1344

224 × 16 1344 0

Multiply by the tens digit.

Add.

224 × 16 1344 2240

224 × 16 1344 + 2240 3584

224 × 16 1344 40

224 × 16 1344 240

There are 3,584 pages printed.

AP P LY Multiply. 1. × +

4 7 1 1

2. ×

5 1 9 2

Level E

3. ×

2 7 3 1

| Chapter 4 - 4

| Lighthouse MATH

4. × +

3 5 3 8 4

Exercise | 4 - 4 Name

Multiply. 1.

99 × 68

81 × 37

63 × 14

13 × 65

52 × 32

564 × 73

829 × 19

283 × 74

756 × 18

10.

2,938 × 42

11. 51 × 22

12. 16 × 83

13. 154 × 78

14. 351 × 18

15. 2,165 × 47

16. 1,943 × 13

Rewrite and multiply.

CH AL L ENGE Solve. 17. Fred made a mistake solving the problem. Look at Fred’s work and find his mistake. Then, find the correct answer.

Level E

| Chapter 4 - 4

| Lighthouse MATH

97 × 56 582 + 485 1,067

4 - 5 | Multiplying by a Three-Digit Number Multiply. 1.

DAILY REV IE W

25 × 34

36 × 47

98 × 33

35 × 68

36 × 21

L E A R N A ND C ONNEC T There are 182 days in a school year. Each school day has 478 minutes. How many minutes of school are there in a school year? To find the total, multiply Multiply by the ones digit.

Add a zero. Erase the numbers you carried. Multiply by the tens digit.

6 1

Add two zeros. Erase the numbers you carried. Multiply by the hundreds digit.

182 × 478 1456

. Add.

182 × 478 1456 12740

182 × 478 1456 12740 72800

182 × 478 1456 12740 72800 86,996

There are 86,996 minutes of school in a school year.

AP P LY Multiply. 1. ×

1 5 5 3 5 7

2. ×

3 8 7 7 6 3

Level E

3. ×

3 0 2 9 6 6

| Chapter 4 - 5

| Lighthouse MATH

4. ×

6 5 8 8 6 3

Exercise | 4 - 5 Name

Multiply. 1.

989 × 257

781 × 267

932 × 997

372 × 806

947 × 482

193 × 917

983 × 624

967 × 757

496 × 768

10.

732 × 741

11. 439 × 556

12. 433 × 209

13. 514 × 508

14. 908 × 756

15. 955 × 614

16. 402 × 744

Rewrite and multiply.

CH AL L ENGE Multiply. 17. 1,568 × 242

Level E

| Chapter 4 - 5

| Lighthouse MATH

4 - 6 | Chapter Review Multiply. 1.

DAILY REV IE W

9 × 5

200 × 40

18 × 7

270 × 32

119 × 25

L E T ' S REV I EW Multiplying by a One-Digit Number

Multiplying by Multiples of 10, 100, and 1,000

56 × 4 224

20 × 6,000 = 120,000 1 zero + 3 zeros = 4 zeros

Multiplying by a Two-Digit Number

Multiplying by a Three-Digit Number

516 24 2064 + 10320 12,384

364 118 2912 3640 + 36400 42,952

AP P LY Use mental math to multiply. 1.

7×2=

9×8=

6×5=

7 × 20 =

9 × 80 =

6 × 50 =

70 × 20 =

90 × 80 =

60 × 50 =

70 × 200 =

90 × 800 =

60 × 500 =

Level E

| Chapter 4 - 6

| Lighthouse MATH

Exercise | 4 - 6 Name

Multiply. 1.

5,000 × 20

8,000 × 400

6,000 × 700

9,000 × 900

2,000 × 2,000

18 × 7

57 × 6

33 × 7

64 × 2

10.

65 × 3

11.

58 × 7

12.

91 × 8

13.

412 × 7

14.

324 × 9

15.

788 × 6

16.

823 × 4

17.

155 × 3

18.

363 × 6

19.

222 × 9

20.

3,086 × 8

21.

4,128 × 3

22.

5,295 × 7

23.

6,276 × 4

24.

6,963 × 7

25.

5,402 × 2

26.

4,160 × 8

27.

51 × 49

28.

54 × 84

29.

26 × 18

30.

25 × 61

31.

58 × 63

32.

93 × 21

33.

54 × 64

34.

836 × 14

35.

497 × 15

36.

426 × 43

37.

374 × 67

38.

864 × 513

39.

326 × 935

40.

549 × 213

Level E

| Chapter 4 - 6

| Lighthouse MATH

Multiply.

4 - 7 | Cumulative Review

Solve. 1.

9 − 2

2 × 1

8 + 3

12 − 8

9 − 6

4 × 2

2 + 2

3 + 6

6 + 3

10.

3 + 2

11.

6 − 3

12.

6 × 2

13.

10 − 7

14.

5 × 3

15.

10 − 9

16.

3 × 8

17.

6 + 4

18.

8 × 2

19.

3 + 8

20.

1 × 5

21.

2 × 4

22.

2 + 9

23.

11 − 8

24.

5 × 2

25.

4 + 5

26.

9 × 8

27.

9 + 4

28.

1 + 1

29.

7 × 2

30.

7 + 6

31.

3 × 4

32.

2 × 5

33.

16 − 7

34.

9 − 7

35.

5 + 9

36.

4 × 6

37. 4 12

38. 4 16

39. 5 25

40. 9 9

41. 9 54

42. 8 16

43. 6 12

44. 7 21

45. 6 18

46. 3 6

47. 7 49

48. 8 24

49. 3 21

50. 5 30

51. 5 40

52. 2 10

53. 4 36

54. 3 9

Level E

| Chapter 4 - 7

| Lighthouse MATH

Exercise | 4 - 7 Name

Add. 1.

426 + 423

712 + 392

657 + 408

3,849 + 8,337

3,996 + 2,435

625 − 71

235 − 160

4,819 − 935

10.

4,954 − 3,444

Subtract. 6.

877 − 499

Multiply. 156 × 3

12.

932 × 4

13.

6,851 × 5

14.

6,368 × 8

15.

23 × 62

16.

78 × 39

17.

456 × 4

18.

95 × 23

19.

987 × 63

20.

27 × 35

21.

52 × 36

22.

6,208 × 6

11.

Round to the highest place value. 23. 4,512

24. 419

25. 87,517

26. 212,471

27. 1,299

28. 718,923

29. 48,911

30. 6,724

Level E

| Chapter 4 - 7

| Lighthouse MATH

5 C H A P T E R

In Chapter 5, we will practice

Division Facts Division is the opposite of multiplication. When we divide, we create equal groups. We can use multiplication facts to help solve division problems. • We will practice dividing by the numbers 2 through 9. • We will learn properties of division. • We will relate multiplication and division with fact families. • We will learn divisibility rules. • We will learn the order of operations.

5 - 1 | Division Facts 2, 3, and 4 Solve. 1.

DAILY REV IE W

7 × 4

9 × 9

3 × 6

5 × 2

6 × 4

L E A R N A ND C ONNEC T Division is the opposite of multiplication. When we divide, we create equal groups. 18 crayons are divided into 3 equal groups. We can find the number of crayons in each group.

18 ÷ 3

3 18

We can use a multiplication fact to help us divide. Think

Solve

What times 3 equals 18?

18 ÷ 3 = 6

3 × 6 = 18

6 3 18

There are 6 crayons in each group.

AP P LY Follow the directions to divide. 1. Circle groups of 3. How many groups?

2. Circle groups of 4. How many groups?

12 ÷ 3 =

8÷4=

3. Circle 2 equal groups. How many in each group?

6÷2=

Vocabulary Dividend - the total amount you start with in a division problem Divisor - the number you are dividing by

Level E

Quotient - the answer to a division problem

| Chapter 5 - 1

| Lighthouse MATH

Exercise | 5 - 1 Name

Divide. 1.

2 6

4 24

4 40

4 32

2 10

3 27

10. 4 44

11. 4 32

12. 4 12

15. 3 15

16. 4 28

17. 2 20

18. 4 16

14. 2 12

3 9

19. 33 ÷ 3 =

20. 18 ÷ 3 =

21. 30 ÷ 3 =

22. 20 ÷ 2 =

23. 36 ÷ 4 =

24. 12 ÷ 2 =

25. 10 ÷ 2 =

26. 14 ÷ 2 =

27. 28 ÷ 4 =

28. 36 ÷ 3 =

29. 9 ÷ 3 =

30. 12 ÷ 4 =

31. 32 ÷ 4 =

32. 12 ÷ 3 =

33. 48 ÷ 4 =

34. 15 ÷ 3 =

35. 40 ÷ 4 =

36. 21 ÷ 3 =

37. 44 ÷ 4 =

38. 16 ÷ 4 =

3 24

13. 4 48

2 14

CH AL L ENGE Solve. 39. 8 × 3 ÷ 4 =

Level E

| Chapter 5 - 1

| Lighthouse MATH

5 - 2 | Division Facts 5, 6, and 7 Solve. DAILY REV IE W

8÷2=

36 ÷ 4 =

18 ÷ 3 =

16 ÷ 4 =

L E A R N A ND C ONNEC T Mr. Ross needs to divide 20 students into groups of 5. How many groups will there be? To find the number of groups, divide by .

20 ÷ 5

5 20 Think

Tip!

Solve

5 times what equals 20?

20 ÷ 5 = 4

5 × 4 = 20

4 5 20

To solve, you can skip count by 5 until 20. The answer is how many 5s you counted.

There will be 4 groups.

AP P LY Follow the directions to divide. 1. Circle 5 equal groups. How many in each group?

2. Circle groups of 6. How many groups?

3. Circle groups of 7. How many groups?

12 ÷ 6 =

28 ÷ 7 =

20 ÷ 5 =

Level E

| Chapter 5 - 2

| Lighthouse MATH

Exercise | 5 - 2 Name

Divide. 1.

5 15

7 28

5 40

7 21

7 70

5 20

10. 7 42

11. 5 35

12. 6 12

15. 6 36

16. 5 40

17. 7 56

18. 6 30

14. 6 18

7 49

19. 49 ÷ 7 =

20. 18 ÷ 6 =

21. 30 ÷ 5 =

22. 24 ÷ 6 =

23. 36 ÷ 6 =

24. 56 ÷ 7 =

25. 28 ÷ 7 =

26. 45 ÷ 5 =

27. 21 ÷ 7 =

28. 35 ÷ 7 =

29. 77 ÷ 7 =

30. 66 ÷ 6 =

31. 50 ÷ 5 =

32. 10 ÷ 5 =

33. 40 ÷ 5 =

34. 60 ÷ 6 =

35. 32 ÷ 4 =

36. 14 ÷ 2 =

37. 16 ÷ 4 =

38. 30 ÷ 3 =

6 24

13. 6 42

7 14

CH AL L ENGE Solve. 39. 5 × 8 ÷ 4 =

Level E

| Chapter 5 - 2

| Lighthouse MATH

5 - 3 | Division Facts 8 and 9 Solve. DAILY REV IE W

12 ÷ 6 =

30 ÷ 5 =

28 ÷ 7 =

25 ÷ 5 =

9 8 72

L E A R N A ND C ONNEC T A farmer picks 72 peaches. A box holds 8 peaches. How many boxes will he need? To find the number of boxes, divide

72 ÷ 8

8 72 Think

Solve

8 times what equals 72?

72 ÷ 8 = 9

8 × 9 = 72 He will need 9 boxes.

AP P LY Follow the directions to divide. 1. Circle groups of 8. How many groups?

2. Circle groups of 9. How many groups?

24 ÷ 8 =

45 ÷ 9 =

Level E

| Chapter 5 - 3

| Lighthouse MATH

Exercise | 5 - 3 Name

Divide. 1.

8 16

9 27

8 40

9 36

8 80

9 81

10. 9 99

11. 9 45

12. 8 32

15. 9 72

16. 4 48

17. 7 56

18. 9 90

14. 9 63

8 48

19. 72 ÷ 8 =

20. 63 ÷ 9 =

21. 32 ÷ 8 =

22. 24 ÷ 8 =

23. 36 ÷ 9 =

24. 56 ÷ 8 =

25. 16 ÷ 8 =

26. 45 ÷ 9 =

27. 18 ÷ 9 =

28. 40 ÷ 8 =

29. 80 ÷ 8 =

30. 64 ÷ 8 =

31. 54 ÷ 9 =

32. 27 ÷ 9 =

33. 90 ÷ 9 =

34. 88 ÷ 8 =

35. 49 ÷ 7 =

36. 24 ÷ 3 =

37. 40 ÷ 4 =

38. 35 ÷ 7 =

8 24

13. 8 88

9 18

CH AL L ENGE Solve. 39. 9 × 4 ÷ 3 =

Level E

| Chapter 5 - 3

| Lighthouse MATH

5 - 4 | Division Properties Solve. DAILY REV IE W

8 64

4 4

7 56

10 ÷ 5 =

30 ÷ 6 =

L E A R N A ND C ONNEC T Any number divided by itself equals 1.

Any number divided by 1 equals itself. There are 4 slices. There is 1 plate. Each plate gets 4 slices.

There are 4 slices. There are 4 plates. Each plate gets 1 slice.

4÷4=1 4×1=4

4÷1=4 1×4=4

0 divided by any number equals 0.

You cannot divide by 0.

There are 0 slices. There are 4 plates. Each plate gets 0 slices.

0÷4=0 4×0=0

There are 4 slices. There are 0 plates. We cannot divide 4 slices between 0 plates.

4÷0=? 0×?=4

Numbers cannot be divided in any order. © Lighthouse Curriculum. Copying strictly prohibited.

There are 4 slices. There are 2 plates. Each plate gets 2 slices.

There are 2 slices. There are 4 plates. Each plate DOES NOT have 2 slices.

4÷2=2

2÷4≠2

AP P LY Follow the directions to divide. 1. Circle one equal group. How many in each group?

2. Circle 6 equal groups. How many in each group?

8÷1=

6÷6=

Level E

| Chapter 5 - 4

| Lighthouse MATH

Exercise | 5 - 4 Name

Divide. 1.

1 8

2 0

9 9

1 6

3 3

1 0

10. 1 5

11. 10 10

12. 1 9

15. 8 0

16. 1 5

17. 4 4

18. 1 7

14. 7 7

1 1

19. 0 ÷ 1 =

20. 5 ÷ 5 =

21. 4 ÷ 1 =

22. 3 ÷ 1 =

23. 0 ÷ 4 =

24. 9 ÷ 9 =

25. 0 ÷ 7 =

26. 8 ÷ 1 =

27. 12 ÷ 1 =

28. 7 ÷ 7 =

29. 0 ÷ 10 =

30. 11 ÷ 1 =

31. 24 ÷ 3 =

32. 32 ÷ 8 =

33. 18 ÷ 2 =

34. 42 ÷ 6 =

35. 63 ÷ 9 =

36. 40 ÷ 8 =

37. 30 ÷ 6 =

38. 48 ÷ 6 =

10 0

13. 1 2

4 0

CH AL L ENGE Solve. 39. (8 ÷ 8) + (0 ÷ 15) + (11 ÷ 1) =

Level E

| Chapter 5 - 4

| Lighthouse MATH

5 - 5 | Multiplication and Division Fact Families Multiply. Check by dividing. 1.

DAILY REV IE W

7 × 4

10 × 6

8 × 1

6 × 9 = 54 9 × 6 = 54

54 ÷ 9 = 6 54 ÷ 6 = 9

5 × 4

L E A R N A ND C ONNEC T A fact family is a group of two multiplication facts and two division facts with the same numbers.

6, 9, 54 6 × 9 = 54 9 × 6 = 54

54 ÷ 9 = 6 54 ÷ 6 = 9

AP P LY

Write the fact family. 1.

21, 3, 7

12, 3, 4

20, 4, 5

30, 5, 6

42, 6, 7

56, 7, 8

72, 8, 9

100, 10, 10

Vocabulary Product - the answer to a multiplication problem Math facts - basic number sentences

Level E

Fact family - a group of related math facts

| Chapter 5 - 5

| Lighthouse MATH

Exercise | 5 - 5 Name

Write the fact family. 1.

8, 2, 4

15, 3, 5

18, 2, 9

21 ÷ 7 =

20, 4, 5

21, 3, 7

Solve. 7.

5÷5=

72 ÷ 9 =

36 ÷ 9 =

10. 3 ÷ 3 =

11. 16 ÷ 4 =

12. 28 ÷ 7 =

13. 30 ÷ 3 =

14. 36 ÷ 4 =

15. 28 ÷ 4 =

16. 44 ÷ 4 =

17. 14 ÷ 7 =

18. 6 ÷ 2 =

19. 54 ÷ 6 =

20. 20 ÷ 4 =

21. 60 ÷ 6 =

22. 40 ÷ 8 =

23. 6 ÷ 2 =

24. 55 ÷ 5 =

25. 2 ÷ 1 =

26. 8 ÷ 1 =

27. 2 ÷ 2 =

28. 12 ÷ 6 =

29. 99 ÷ 9 =

30. 3 ÷ 3 =

31. 30 ÷ 3 =

32. 40 ÷ 5 =

33. 35 ÷ 7 =

CH AL L ENGE Find the missing number in each fact family. 34. 81,

35. 144,

Level E

| Chapter 5 - 5

, 12

| Lighthouse MATH

5 - 6 | Divisibility Rules Solve. DAILY REV IE W

6 24

6 6

8 56

16 ÷ 4 =

20 ÷ 5 =

L E A R N A ND C ONNEC T Use these rules to know if a number can be divided without any left over.

A number is divisible by...

if it ends with 0, 2, 4, 6, or 8.

if the sum of its digits is 3, 6, or 9. If the sum has more than one digit, add them again.

if it ends with a 0 or a 5.

if the sum of its digits is 9. If the sum has more than one digit, add them again.

if it ends with a 0.

AP P LY Which numbers can 24 be divided by with none left over? 1.

Does 24 end with 0, 2, 4, 6, or 8?

Is 24 divisible by 2?

Does 24 equal 3, 6, or 9 when you add up all its digits?

Is 24 divisible by 3?

Does 24 end with a 0 or a 5?

Is 24 divisible by 5?

Does 24 equal 9 when you add up all its digits?

Is 24 divisible by 9?

Does 24 end with a 0?

Is 24 divisible by 10?

Level E

| Chapter 5 - 6

| Lighthouse MATH

Exercise | 5 - 6 Name

10.

11.

12.

13.

14.

15.

16.

Read the problem. Then solve. 17. There are 30 chocolates. Can they be packaged in groups of 2, 3, 5, 9, or 10? List all the possibilities.

18. A class has 36 students. Can the teacher divide them into groups of 2, 3, 5, 9, or 10? List all the possibilities.

CH AL L ENGE 19. Any number divisible by 8 is also divisible by 2 and 4. Explain why.

Level E

| Chapter 5 - 6

| Lighthouse MATH

For each number, circle the number or numbers it is divisible by. Hint: There may be no correct numbers to circle.

5 - 7 | Order of Operations Find the fact family. 1.

15, 3, 5

64, 8, 8

28, 4, 7

30, 5, 6

DAILY REV IE W

L E A R N A ND C ONNEC T To solve this number sentence, we need to follow a set order of operations so that we all get the same answer.

10 − 14 ÷ 7 + 1 Do the multiplication and division from left to right. Do the addition and subtraction from left to right.

10 − 14 ÷ 7 + 1 10 − 2 + 1 10 - 2 + 1 8+1

AP P LY Solve. 1.

4 + 12 − 7

2+3×2

10 − 4 ÷ 2

5×2+1

9+3×2

8 + 10 ÷ 5

6×2÷4

20 − 5 × 3

10. 4 + 4 × 4

Vocabulary Evaluate - to solve an algebraic expression to find its simplified value

Level E

| Chapter 5 - 7

| Lighthouse MATH

12 ÷ 3 − 2

Exercise | 5 - 7 Name

Solve. 1.

3+2×5

10 ÷ 2 + 4

15 − 3 × 2

4×3÷2

2×5+3×2

20 − 10 ÷ 5

8+4−2+1

3×2+4

5+5×5−5

10. 10 − 2 + 3 + 7

11. 2 × 2 × 2 × 2

12. 18 ÷ 2 − 4 + 1

13. 12 − 10 ÷ 5

14. 7 × 1 + 8 ÷ 2

15. 10 + 10 ÷ 10 + 10

16. 4 × 10 ÷ 2

17. 15 − 5 − 5 − 5

18. 2 × 3 + 4 × 1

19. 8 + 2 × 6 − 4

20. 30 ÷ 3 ÷ 2

21. 12 + 8 ÷ 2 + 3

22. 5 × 4 − 3 × 2

23. 10 + 10 ÷ 2 × 2

24. 9 − 4 + 6 ÷ 2

26. A teacher has 5 pencils and 2 boxes with 10 pencils in each box. How many pencils does she have in all?

25. Danny had $20. He bought 3 slices of pizza that each cost $5. He also bought a drink for $4. How much money does he have left?

CH AL L ENGE Parentheses ( ) can be used to group numbers that should be solved first. Write parentheses in the number sentence to group numbers so that it is equal to 16. 27. 4 + 6 × 2 − 15 ÷ 3 + 1

Level E

| Chapter 5 - 7

| Lighthouse MATH

Read the problem. Write a number sentence. Then solve.

5 - 8 | Chapter Review Solve. 1. 6×8−4÷2

DAILY REV IE W

2. 6 × (8 − 4) ÷ 2

3. 6 × (8 − 4 ÷ 2)

4. (6 × 8) − (4 ÷ 2)

L E T ' S REV I EW Division

Division Properties and Rules

When we divide, we create equal groups. Use a multiplication fact to solve a division problem.

A number divided by 1 equals itself. A number divided by itself equals 1. 0 divided by a number equals 0. You cannot divide by 0.

20 ÷ 4 = 5 5 × 4 = 20

Order of Operations First, solve multiplication and division from left to right. Then, solve addition and subtraction from left to right.

12 − 4 + 6 ÷ 2 12 − 4 + 3

8+3 11

AP P LY Divide. 1.

2 18

4 24

8 80

9 27

7 7

6 18

10. 2 12

100

Level E

| Chapter 5 - 8

8 16

| Lighthouse MATH

5 60

11. 8 32

7 21

12. 9 54

Exercise | 5 - 8 Name

Divide. 1.

5 25

9 72

9 63

4 44

3 15

9 18

10. 5 25

11. 4 44

12. 8 64

15. 1 6

16. 6 18

17. 6 24

18. 7 56

13. 5 50

14. 7 49

3 33

1 1

19. 45 ÷ 5 =

20. 8 ÷ 4 =

21. 12 ÷ 2 =

22. 81 ÷ 9 =

23. 0 ÷ 6 =

24. 7 ÷ 7 =

25. 10 ÷ 1 =

26. 28 ÷ 7 =

1 2

27. 24, 8, 3

28. 35, 7, 5

29. 72, 9, 8

30. 48, 8, 6

Write the fact family. 31. 20, 5, 4

Solve. 32. 3 + 9 × 3 − 1

33. 12 − 8 + 3 × 6

Level E

| Chapter 5 - 8

34. 18 + 17 − 4 × 5

| Lighthouse MATH

35. 38 − 2 × 7 + 16

101

5 - 9 | Cumulative Review

Solve. 1.

8 + 4

8 + 7

13 − 5

3 × 5

5 × 7

9 × 7

7 + 9

9 − 7

3 × 2

10.

3 × 6

11.

6 − 3

12.

4 × 6

13.

9 + 7

14.

5 × 4

15.

4 + 1

16.

9 + 5

17.

8 − 5

18.

12 − 5

19.

7 + 1

20.

10 − 3

21.

12 − 4

22.

1 + 8

23.

2 + 6

24.

10 − 5

25.

3 + 2

26.

4 × 9

27.

3 × 5

28.

9 − 8

29.

6 + 7

30.

9 + 3

31.

14 − 9

32.

5 × 3

33.

2 × 6

34.

1 + 9

35.

3 − 1

36.

7 × 8

37.

13 − 4

38.

14 − 5

39.

3 + 9

40.

1 + 7

41.

6 − 1

42.

6 + 2

43.

2 + 3

44.

8 × 2

45.

9 − 1

46.

4 + 2

47.

9 × 6

48.

2 + 5

49. 4 32

50. 8 64

51. 4 16

52. 3 3

53. 7 28

54. 8 24

55. 4 28

56. 5 35

57. 9 81

58. 2 18

59. 1 7

60. 4 24

61. 9 27

62. 5 45

63. 3 9

64. 3 27

65. 6 18

66. 2 2

102

Level E

| Chapter 5 - 9

| Lighthouse MATH

Exercise | 5 - 9 Name

Add. 1.

661 + 123

868 + 971

619 + 629

3,019 + 8,122

6,742 + 4,288

949 − 561

850 − 728

5,851 − 2,187

10.

8,178 − 3,179

12.

71 × 2

13.

310 × 8

14. 655 × 4

15.

16 × 89

Subtract. 6.

787 − 268

Multiply. 11.

22 × 4

16. 5 25

17. 7 49

18. 9 54

19. 6 42

20. 6 30

21. 9 45

22. 1 2

23. 9 18

24. 8 32

25. 6 36

26. 6 54

27. 9 36

Divide.

Compare. Write < or > in the circle. 28. 24 31. 28,933

29. 423

28,800

418

32. 635,882

Level E

| Chapter 5 - 9

635,818

| Lighthouse MATH

30. 7,500

7,499

33. 6,421

6,471

103

6 C H A P T E R

104

In Chapter 6, we will learn about

Long Division When we divide large numbers, we follow a set of steps to make dividing easier. We work on the numbers from left to right. • We will learn the steps of long division. • We will divide with remainders. • We will interpret remainders. • We will find quotients with one, two, and three digits, including quotients with zeros. • We will learn how to decide where to start dividing. • We will learn how to divide by a two-digit number.

105

6 - 1 | One-Digit Quotients with Remainders Solve. DAILY REV IE W

4 36

5 40

3 12

9 54

8 56

L E A R N A ND C ONNEC T A box of 26 pencils needs to be divided among 3 students. How many pencils will each student get and how many will be left over? To find the number of pencils each student will get, divide by . The amount left over is called the remainder.

quotient

remainder

8 R2 3 26 divisor

dividend

D Divide.

M Multiply.

S Subtract.

R Remainder.

8 3 26

8 3 26 24

8 3 26 − 24 2

8 R2 3 26 − 24 2

26 − 24 = 2 Make sure 2 < 3

Write the remainder (the amount left over).

How many times does 3 fit into 26?

8 × 3 = 24

3 × 8 = 24 3 × 9 = 27

The remainder must always be less than the divisor.

It fits 8 times.

Each student will get 8 pencils. There will be 2 left over.

AP P LY Fill in the missing numbers. 1.

4 3 3 −

R 7 4 1 −

R 5 2 3 −

R 8 7 5 −

Vocabulary Divisor - the number doing the dividing Dividend - the number that is being divided

106

Quotient - the answer to a division problem Remainder - the amount left over after dividing into equal groups

Level E

| Chapter 6 - 1

| Lighthouse MATH

Exercise | 6 - 1 Name

Divide. 1.

5 21

6 13

7 47

3 17

8 63

2 11

9 39

6 52

2 13

10. 4 39

12. 2 13

13. 4 39

14. 6 52

16. 57 ÷ 9

17. 29 ÷ 4

18. 41 ÷ 7

11. 6 52

Remember: The remainder must be less than the number you are dividing by.

15. 48 ÷ 5

Read the problem. Then solve. 20. Eric has 22 books to put on his bookcase. Each shelf can hold 5 books. How many shelves will he fill? How many books will be left over?

19. Mike has 35 taffies that he wants to divide evenly among 8 people. How many taffies will each person get, and how many will be leftover?

CH AL L ENGE Use mental math to solve. 21. 29 ÷ 3 =

22. 39 ÷ 7 =

Level E

| Chapter 6 - 1

23. 46 ÷ 9 =

| Lighthouse MATH

24. 52 ÷ 6 =

107

Rewrite and solve.

6 - 2 | Interpreting Remainders Solve. DAILY REV IE W

4 37

7 46

3 14

9 67

8 69

L E A R N A ND C ONNEC T There are 47 ounces of juice in a bottle. Eitan wants to pour 8 ounces of juice into each cup. To answer a division question, we need to decide how to use the remainder in our answer. We can drop it, use it, or round our answer up. Read the question and decide what makes sense. How many 8-ounce cups can he fill?

How much juice will be left over?

How many cups does Eitan need?

Drop it

Use it

Round up

We drop the remainder from the answer.

The remainder is our answer.

Eitan can fill 5 cups.

There will be 7 ounces left over.

The extra 7 ounces won’t fill an 8-ounce cup.

We add one to the answer and drop the remainder.

Eitan needs 6 cups. He needs 5 cups, plus one more for the extra 7 ounces.

A P P LY Read the question. Circle what to do with the remainder. Answer the question. 1. A farmer packs 52 apples into boxes for market. Each box holds 6 apples. How many apples are left over? 8R4 6 52

108

Round up Use it Drop it

Level E

| Chapter 6 - 2

2. 29 campers need to sleep in tents. If 8 campers fit in each tent, how many tents are needed? 3R5 8 29

| Lighthouse MATH

Round up Use it Drop it

Exercise | 6 - 2 Name

1. Aaron puts 47 oranges into bags that hold 5 oranges each. How many full bags can he make?

2. The teacher lines up 29 students in rows of 4 for an activity. How many students are left over?

3. Ben buys 31 cards. Each booklet holds 6 cards. How many booklets does he need?

4. Anna plants 24 flowers in rows of 9. How many full rows can she plant?

5. Max has 53 toy cars. He puts 8 cars on each shelf. How many shelves are completely filled?

6. The school librarian places 35 books in bins that hold 4 books each. How many bins are needed?

7. Rachel bakes 41 cookies. She puts 6 cookies on each plate. How many cookies are not on a full plate?

8. There are 50 pencils in the classroom. The teacher packs them in boxes of 7. How many full boxes are there?

9. The gardener has 73 plants to plant in rows of 9. How many plants are left over?

10. Paul is loading 39 workers into trucks. Each truck holds 6 workers. How many trucks are needed?

CH AL L ENGE Solve. 11. The school orders 24 red notebooks, 19 blue notebooks, and 18 yellow notebooks. The notebooks are placed into boxes that each hold 7 notebooks. How many boxes are needed?

Level E

| Chapter 6 - 2

| Lighthouse MATH

109

Read the problem. Decide what to do with the remainder. Answer the question.

6 - 3 | Two-Digit Quotients Solve. DAILY REV IE W

7 60

3 20

5 48

7 24

L E A R N A ND C ONNEC T There are 54 seeds in a packet. Eli wants to plant 4 rows of seeds. How many seeds will be in each row? How many seeds will be left over? To find how many seeds go in each row, divide

Divide the tens. 1 4 54 − 4 14

Divide the ones. 13 R2 4 54 − 4 14 − 12 2

D Divide

4 fits into 5: 1 time

D Divide

4 fits into 14: 3 times

M Multiply

1×4=4

M Multiply

3 × 4 = 12

S Subtract 5 − 4 = 1

S Subtract 14 − 12 = 2

Make sure 1 < 4

Check that 2 < 4

R Remainder There are 2 left over.

B Bring Down The ones digit (4).

He will plant 13 seeds in each row. 2 seeds will be left over.

AP P LY Divide. 1.

3 4 4 −

3. 8 9 6 −

R 5 6 7 −

Vocabulary Quotient - The solution to a division problem

110

Level E

| Chapter 6 - 3

| Lighthouse MATH

R 6 9 2 −

Exercise | 6 - 3 Name

Divide. 1.

3 84

9 95

4 96

5 75

3 63

6 72

4 62

5 90

10. 7 91

14. 2 87

15. 3 72

11. 4 83

12. 3 96

13. 3 75

4 85

Rewrite and solve. 17. 90 ÷ 5

18. 99 ÷ 3

19. 85 ÷ 2

Read the problem. Then solve. 20. Aaron picks 84 peppers. He divides the peppers equally into 6 bags. How many peppers are in each bag?

21. Emma has 80 grape tomatoes. She puts 3 tomatoes on each plate. How many complete plates can she make?

CH AL L ENGE Solve. 22. How many times does 8 fit into 1,680?

Level E

| Chapter 6 - 3

| Lighthouse MATH

111

16. 95 ÷ 3

6 - 4 | Three-Digit Quotients Solve. DAILY REV IE W

3 84

9 99

3 96

L E A R N A ND C ONNEC T There are 565 nails in a box. Steven uses 5 nails in each project. How many projects can he make? To find how many projects he can make, divide by . Divide the hundreds. 1 5 565 − 5 06

Divide the tens. 11 5 565 − 5 06 − 5 15

Divide the ones. 113 5 565 − 5 06 − 5 15 − 15 0

D Divide 5 fits into 5:

D Divide 5 fits into 6:

D Divide 5 fits into 15:

1 time

M Multiply

1 time

1×5=5

M Multiply

3 × 5 = 15

S Subtract 5 − 5 = 0

S Subtract 6 − 5 = 1

S Subtract 15 − 15 = 0

B Bring down The tens digit

B Bring down The ones

R Remainder There are

0<5

1<5

(6).

1×5=5

3 times

M Multiply

0<5

none left over.

digit (5).

He can make 113 projects.

AP P LY Divide. 1.

112

3 9 3 6 −

4 8 6 3 −

5 9 7 5 −

2 7 2 7 −

−

Level E

| Chapter 6 - 4

| Lighthouse MATH

Exercise | 6 - 4 Name

Divide. 1.

3 936

5 724

4 848

4 964

3 999

3 756

6 671

7 924

10. 4 864

4 887

Rewrite and solve. 11. 735 ÷ 5

12. 917 ÷ 9

13. 864 ÷ 6

14. 672 ÷ 3

15. Leo pays $975 for five bikes. Each bike is the same price. How much does each bike cost?

Read the problem. Then solve. 16. There are 642 fish divided equally among three tanks at the aquarium. How many fish are in each tank?

CH AL L ENGE Solve. 17. Mr. Levine has 6 children. He divides $429 evenly between them. How much money does each child get? Hint: Divide the $3 lef tover between the 6 children.

Level E

| Chapter 6 - 4

| Lighthouse MATH

113

6 - 5 | Deciding Where to Start Dividing Solve. DAILY REV IE W

5 726

4 851

4 964

4 887

L E A R N A ND C ONNEC T There are 126 horses on a farm. Each stable holds 6 horses. How many stables do they need? To find how many stables they need, divide by Decide where to start dividing.

Divide the tens.

Divide the ones.

2 6 126 − 12 06

21 6 126 − 12 06 − 6 0

You can put an x above the place you cannot divide. x 6 126

D Divide 6 fits into 12:

2 times

M Multiply

6 does not fit into 1. 6 can fit into 12.

2 × 6 = 12

1 time

M Multiply

1×6=6

S Subtract 12 − 12 = 0

S Subtract 6 − 6 = 0

B Bring down The ones

R Remainder There are

0<6

none left over.

digit (6).

D Divide 6 fits into 6:

They need 21 stables.

AP P LY Divide. 1.

8 6 7 2 − −

5 3 1 2 −

−

7 9 6 6 − − −

114

Level E

| Chapter 6 - 5

| Lighthouse MATH

4 2 3 5 − −

Exercise | 6 - 5 Name

Divide. 1.

9 693

9 864

7 643

3 819

2 782

9 823

3 672

3 474

10. 4 364

9 756

Rewrite and solve. 12. 531 ÷ 9

13. 899 ÷ 6

14. 273 ÷ 3

11. 884 ÷ 4

Read the problem. Then solve. 15. The Ross family drove 648 miles this summer. They drove the same number of miles on each of the 6 days of their trip. How many miles did they drive each day?

16. The class library has 126 books to put on 9 shelves. How many books will go on each shelf?

CH AL L ENGE 17. Anna ordered 277 beads to make bracelets. She can put 22 beads on each bracelet. How many beads will not fit evenly on a bracelet?

Level E

| Chapter 6 - 5

| Lighthouse MATH

115

6 - 6 | Zeros in the Quotient Solve. DAILY REV IE W

5 493

4 932

383 ÷ 4

533 ÷ 9

L E A R N A ND C ONNEC T There are 624 flowers in 6 sections of the flower farm. How many flowers are in each section? To find out how many flowers are in each section, divide Divide the hundreds. 1 6 624 − 6 02

Divide the tens. 10 6 624 − 6 02 − 0 24

. Divide the ones. 1 04 6 624 − 6 02 − 0 24 − 24 0

D Divide 6 doesn’t fit D Divide 6 fits into 6:

1 time

M Multiply

1×6=6

D Divide 6 fits into 24:

0×6=0

M Multiply

4 times

4 × 6 = 24

S Subtract 6 − 6 = 0

S Subtract 2 − 0 = 2

S Subtract 24 − 24 = 0

B Bring down The tens

B Bring down The ones

R Remainder There are

2<6

0<6

digit (4).

digit (2).

into 2. Write a 0 above the 2.

none left over.

There are 104 flowers in each section.

AP P LY Divide. 1.

5 5 1 5 − −

116

9 6 3 0 − −

Level E

7 7 2 2 −

−

| Chapter 6 - 6

| Lighthouse MATH

4 2 0 5 − −

Exercise | 6 - 6 Name

Divide. 1.

3 324

5 603

9 810

8 864

6 612

7 735

7 706

5 525

10. 9 945

8 642

Rewrite and solve. 12. 842 ÷ 7

13. 913 ÷ 3

14. 720 ÷ 6

Read the problem. Then solve. 15. Emma has 114 markers. She organizes them into 6 bins. How many markers will be in each bin?

16. The zoo orders 816 pounds of food for 4 giraffes. How many pounds of food can each giraffe get?

CH AL L ENGE 17. A tow truck is carrying two identical cars that weigh 5,004 pounds in total. How much does each car weigh?

Level E

| Chapter 6 - 6

| Lighthouse MATH

117

11. 308 ÷ 4

6 - 7 | Dividing by Multiples of Ten Solve. DAILY REV IE W

3 423

5 505

9 910

8 760

L E A R N A ND C ONNEC T There are 458 books in the library. Each shelf holds 50 books. How many full shelves are there? To find the number of shelves, divide

Divide the ones.

Decide where to start dividing.

Finish the steps of long division.

9 50 458

You can put x’s above the places you cannot divide.

xx 50 458

9 R8 50 458 − 450 8

D Divide

M Multiply

How many times does 50 fit into 458?

50 does not fit into 4 or 45. 50 can fit into 458. © Lighthouse Curriculum. Copying strictly prohibited.

50 × 9 = 450 50 × 10 = 500

9 × 50 = 450 S Subtract

458 − 450 = 8 Make sure 8 < 50 R Remainder

It fits 9 times.

There are 8 left over.

There are 9 full shelves.

AP P LY Divide. 1.

118

20 1 4 0 −

70 6 5 0 −

Level E

| Chapter 6 - 7

30 1 3 6 −

| Lighthouse MATH

90 7 5 6 −

Exercise | 6 - 7 Name

Divide. 1.

40 880

30 264

20 380

40 456

30 648

80 600

60 900

70 825

10. 20 600

14. 60 490

15. 40 936

11. 80 864

12. 30 702

13. 20 177

50 735

Rewrite and solve. 17. 842 ÷ 70

18. 913 ÷ 30

19. 720 ÷ 60

16. 300 ÷ 40

Read the problem. Then solve. 20. Fred got paid $580 for 20 hours of work. How much money did Fred make per hour?

21. 768 cans are packed into boxes that hold 40 cans each. How many full boxes can be packed? How many cans will be left over?

CH AL L ENGE 22. There are 1,225 seats in the multipurpose room. Each row has 35 seats. How many rows of seats are there?

Level E

| Chapter 6 - 7

| Lighthouse MATH

119

6 - 8 | Dividing by Two-Digit Numbers Solve. DAILY REV IE W

40 840

20 260

30 385

40 450

L E A R N A ND C ONNEC T Frank needs to pay $144 to a friend over 18 months. He will pay the same amount each month. How much money will he pay his friend each month? To find how much he will pay each month, divide by . Decide where to start dividing.

Divide the ones.

Finish the steps of long division.

8 18 144

8 18 144 − 144 0

You can put x’s above the places you cannot divide.

xx 18 144

D Divide

How many times does 18 fit into 144?

18 does not fit into 1 or 14. 18 fits into 144. © Lighthouse Curriculum. Copying strictly prohibited.

M Multiply

18 × 8 = 144

18 × 8 = 144 S Subtract

144 − 144 = 0 Make sure 0 < 18 R Remainder

It fits 8 times.

There are none left over.

He will pay $8 each month.

AP P LY Divide. 1.

120

18 1 6 2 −

24 1 9 2 −

Level E

| Chapter 6 - 8

16 1 4 4 −

| Lighthouse MATH

27 2 1 6 −

Exercise | 6 - 8 Name

Divide. 1.

42 126

27 135

36 144

98 882

63 189

45 135

84 756

76 684

10. 72 576

14. 66 594

15. 72 576

11. 39 195

12. 38 152

13. 35 140

96 768

Rewrite and solve. 17. 192 ÷ 48

18. 162 ÷ 54

19. 672 ÷ 84

16. 168 ÷ 56

Read the problem. Then solve. 20. A farmer picks 558 apples. He packs them into baskets that hold 62 apples each. How many baskets can he fill?

21. A school ordered 252 pencils. Each classroom receives 36 pencils. How many classrooms will receive pencils?

CH AL L ENGE 22. Molly needs 1,255 cookies for the bake sale. She can make 95 cookies each day. How many days will she need to bake all of the cookies?

Level E

| Chapter 6 - 8

| Lighthouse MATH

121

6 - 9 | Dividing by Two-Digit Numbers with Remainders Solve. DAILY REV IE W

42 168

27 162

36 180

98 784

L E A R N A ND C ONNEC T Pat picked 367 avocados. He puts them into boxes that can each fit 48 avocados. How many boxes does he need? To find how many boxes he needs, divide .

Divide the ones.

Decide where to start dividing.

Finish the steps of long division.

7 48 367

You can put x’s above the places you cannot divide.

xx 48 367

7 R31 48 367 − 336 31

D Divide

M Multiply

How many times does 48 fit into 367?

48 does not fit into 3 or 36. 48 fits into 367.

48 × 7 = 336 48 × 8 = 384

48 × 7 = 336 S Subtract

367 − 336 = 31 Make sure 31 < 48 R Write the remainder

It fits 7 times.

There are 31 left over.

He needs 8 boxes.

AP P LY Divide. 1.

122

18 1 7 9 −

24 2 6 −

Level E

| Chapter 6 - 9

75 6 7 8 −

| Lighthouse MATH

75 8 7 −

Exercise | 6 - 9 Name

Divide. 1.

34 56

47 389

36 274

42 315

67 384

71 298

43 78

84 718

10. 85 768

14. 53 428

15. 37 84

11. 44 346

12. 43 285

13. 53 437

58 245

Rewrite and solve. 16. 68 ÷ 22

17. 689 ÷ 76

18. 518 ÷ 67

19. 295 ÷ 64

20. There are 97 students in the fifth grade. Each classroom can hold up to 29 students. How many classrooms do they need?

Read the problem. Then solve. 21. A factory produced 234 toys. Each shipping crate can hold 76 toys. How many full crates can be packed?

CH AL L ENGE 22. A camp is going on a trip. Each bus can hold 93 campers. There are 4,870 campers. How many buses will be packed full? How many campers will be on the last bus?

Level E

| Chapter 6 - 9

| Lighthouse MATH

123

6 - 10 | Two-Digit Quotients with Two-Digit Divisors Solve. DAILY REV IE W

36 56

52 388

36 354

92 415

L E A R N A ND C ONNEC T A construction company has 1,872 bricks to use for a new sidewalk. Each section of sidewalk needs 36 bricks. How many sections of sidewalk can they make? Decide where to start dividing. You can put x’s above the places you cannot divide.

xx 36 1872

Divide the tens.

Divide the ones.

5 36 1872 − 180 72

52 36 1872 − 180 72 − 72 0

D Divide 36 fits into 187:

D Divide 36 fits into 72:

5 times

M Multiply

36 does not fit into 1 or 18. 36 fits into 187.

2 times

5 × 36 = 180

M Multiply

S Subtract 72 − 72 = 0

B Bring down The ones

R Remainder There are

7 < 36

0 < 36

none left over.

digit (2).

36 × 2 = 72

S Subtract 187 − 180 = 7

They can make 52 sections.

AP P LY Divide. 1.

124

12 8 6 4 −

Level E

24 1 2 4 8 −

| Chapter 6 - 10

| Lighthouse MATH

21 1 7 6 0 −

Exercise | 6 - 10 Name

Divide. 1.

14 728

15 945

24 816

22 990

32 1,628

25 1,584

36 1,000

48 1,347

10. 64 1,272

26 858

Rewrite and solve. 12. 148 ÷ 14

13. 846 ÷ 27

14. 1,248 ÷ 24

11. 342 ÷ 17

Read the problem. Then solve. 15. A school buys 1,344 notebooks. Each classroom gets 32 notebooks. How many classrooms can get notebooks?

16. There are 985 pages in a book. Dina wants to read 25 pages each day. How many days will it take her to finish the book?

CH AL L ENGE 17. A factory makes 1,005 water bottles. The bottles are packed into boxes that hold 36 bottles each. How many boxes are needed?

Level E

| Chapter 6 - 10

| Lighthouse MATH

125

6 - 11 | Chapter Review Solve. DAILY REV IE W

24 928

28 2,654

26 2,184

41 2,993

L E T ' S REV I EW Look at the highest place value to decide where to start dividing. Then, work from left to right on the steps of long division. quotient

Divide.

Write your answer above the line.

Multiply.

The answer you just wrote by the divisor.

Subtract. Check that the remainder is less than the divisor. Bring down.

divisor

The next digit to the right.

Remainder. If there are any left over, write the number next to the answer after the letter R.

remainder

308 R2 4 1234 − 12 03 − 0 34 − 32 2

dividend

What to do with a remainder:

Round the quotient up: If all of what you divided must be included. Drop the remainder: If you are looking for how many whole or full parts. Use the remainder: If you are looking for how much is left over.

AP P LY Divide. 1.

6 5 6 0 − −

126

7 1 0 2 6 −

5 1 6 3 5 −

4 2 5 0 4 −

−

Level E

| Chapter 6 - 11

| Lighthouse MATH

Exercise | 6 - 11 Name

Divide. 1.

11 770

52 704

38 988

16 640

83 340

48 4,070

44 800

64 3,579

10. 76 4,004

80 2,000

Rewrite and solve. 12. 1,974 ÷ 21

13. 570 ÷ 8

14. 2,635 ÷ 31

11. 2,070 ÷ 90

Read the problem. Then solve. 15. A school ordered 1,248 pencils to pack into boxes that hold 18 pencils each. How many full boxes can be packed?

16. A farmer picks 1,375 apples and puts them into crates that hold 24 apples each. How many crates are needed to hold all the apples?

17. A camp has 1,453 water bottles to divide equally among 22 bunks. How many bottles will be left over after sharing equally?

18. A factory packs 1,936 toy cars in boxes of 27 cars each. How many boxes are needed for all the cars?

Level E

| Chapter 6 - 11

| Lighthouse MATH

127

6 - 12 | Cumulative Review

Solve. 1.

7 − 3

9 + 3

8 × 8

4 − 3

2 + 7

1 × 6

4 − 1

4 × 8

1 + 7

10.

7 × 7

11.

2 × 9

12.

11 − 5

13.

3 + 6

14.

3 × 8

15.

1 + 3

16.

2 × 2

17.

1 + 9

18.

5 − 2

19.

2 × 3

20.

1 × 2

21.

8 + 7

22.

9 × 5

23.

4 × 4

24.

8 × 2

25.

6 + 8

26.

4 + 7

27.

3 + 7

28.

1 × 1

29.

11 − 2

30.

7 × 4

31.

9 − 6

32.

1 + 6

33.

5 × 7

34.

5 × 6

35.

15 − 7

36.

6 × 2

37. 2 14

38. 7 49

39. 3 15

40. 3 12

41. 5 20

42. 2 16

43. 5 45

44. 2 12

45. 1 5

46. 2 2

47. 8 72

48. 7 21

49. 8 64

50. 2 4

51. 1 3

52. 3 21

53. 9 18

54. 6 6

128

Level E

| Chapter 6 - 12

| Lighthouse MATH

Exercise | 6 - 12 Name

Add. 1.

360 + 695

750 + 689

385 + 636

5,889 + 8,035

6,867 + 5,600

845 − 493

951 − 685

5,347 − 3,272

10.

6,108 − 422

12.

769 × 7

13.

7,427 × 7

14.

6,027 × 6

15.

28 × 44

Subtract. 6.

697 − 190

Multiply. 11.

287 × 7

Divide. 17. 5 382

18. 3 387

19. 6 4,787

20. 22 947

16. 7 497

Solve. 21. 4 × (3 + 1) − 15

22. 12 + (8 − 1)

23. (3 + 4) × 4

24. 15 − (2 × 5) + 2

25. 20 − 3 + (2 × 4)

26. (5 + 1) × (8 − 5)

27. 10 × 2 − 7

28. 18 − 3 + (4 × 5)

Level E

| Chapter 6 - 12

| Lighthouse MATH

129

7 C H A P T E R

130

In Chapter 7, we will learn about

Fractions Fractions are numbers that show parts of a whole. They can be less than one, equal to one, or greater than one. • We will review how to write a fraction. • We will find equivalent fractions using pictures, multiplication and division. • We will put fractions in their simplest form. • We will find equivalent fractions with common denominators. • We will compare fractions. • We will understand improper fractions and mixed numbers.

131

7 - 1 | Understanding Fractions Divide. DAILY REV IE W

4 58

3 63

12 492

5 521

L E A R N A ND C ONNEC T Fractions are numbers that show parts of a whole. To find a fraction, divide a whole into equal parts. The bottom number of the fraction tells us how many equal parts there are. Fraction that is red:

The garden is divided into 4 equal parts.

Each part 1 is of the 4 garden.

red parts

equal parts

1 of the garden is red. 4 We say one quarter.

AP P LY Write the number of equal parts. Write the fraction for each part. 1.

2 equal parts Each part is

equal parts

Each part is

equal parts Each part is

equal parts

Each part is

132

equal parts Each part is

Level E

| Chapter 7 - 1

| Lighthouse MATH

equal parts Each part is

Exercise | 7 - 1 Name

What part is colored red? Circle the correct fraction. 1.

1 2

1 3

1 6

1 4

1 3

1 5

1 4

1 2

1 3

1 6

1 4

1 3

1 8

1 4

1 2

1 8

1 2

1 8

1 6

1 8

1 2

1 6

Color the correct fraction. 10.

11.

1 10

13.

1 8

12.

1 4

14.

1 3

15.

1 10

1 5

16.

1 3

1 4

CH AL L ENGE Divide each square into 4 equal parts. Each way must be different. 17.

18.

Level E

| Chapter 7 - 1

19.

| Lighthouse MATH

133

7 - 2 | Writing Fractions What fraction is shaded? 1.

DAILY REV IE W

L E A R N A ND C ONNEC T A fraction can show parts of a whole:

A fraction can show parts of a set:

The cake was divided into 8 equal slices. There are 3 slices left.

There are 5 ducks. 2 of them are blue.

We can write the fraction of cake left.

Slices left Equal parts

We can write the fraction of ducks that are blue.

numerator

Blue ducks

denominator

All the ducks

There are three-eighths of the cake left.

numerator

denominator

Two-fifths of the ducks are blue.

AP P LY Write the fraction the picture shows. 1.

Vocabulary Numerator - the top number that shows how many parts of the whole Denominator - the bottom number below the fraction bar that shows how many equal parts make the whole

134

Level E

| Chapter 7 - 2

| Lighthouse MATH

Exercise | 7 - 2 Name

Shade each fraction. 1.

5 9

2 3

1 5

3 4

5 6

3 6

3 5

2 3

10.

4 12

1 2

11.

12.

13.

14.

15.

16.

17.

18.

Write each fraction.

CH AL L ENGE Draw both fractions. Circle the bigger fraction. 19. 1

1 8

Level E

| Chapter 7 - 2

| Lighthouse MATH

135

7 - 3 | Equivalent Fractions Write the fraction. 1.

DAILY REV IE W

L E A R N A ND C ONNEC T Two or more fractions can show the same amount. We call them equivalent fractions. We can use a picture to make equivalent fractions. Color the number of pieces that show the same amount.

1 2 of a cake

2 4 of a cake

? 8 of a cake

1 2 4 1 2 4 , , and are equivalent fractions. = = 2 4 8 2 4 8

When we color 4 slices in the last cake, it shows the same amount as 21 and 42 .

AP P LY Shade to find an equivalent fraction. 1.

2 3

2 8

2 4

Vocabulary Equivalent fractions - fractions that represent the same amount

136

Level E

| Chapter 7 - 3

| Lighthouse MATH

Exercise | 7 - 3 Name

Look at the pictures. Write the missing numerators. 1.

Shade to find an equivalent fraction. 8.

3 4

6 24

= 10.

3 6

11.

12 20

= © Lighthouse Curriculum. Copying strictly prohibited.

4 16

CH AL L ENGE Solve. 12. Find three fractions that are equivalent to three-fourths.

Level E

| Chapter 7 - 3

| Lighthouse MATH

3 4 =

137

7 - 4 | Finding Equivalent Fractions Color the number of parts that show the same amount. Write the missing numerator. 1.

DAILY REV IE W 1 2 = 8

2 3 = 6

3 4 = 8

L E A R N A ND C ONNEC T To find an equivalent fraction, we can multiply the numerator and denominator by the same number. Whatever you do to the top, you must do to the bottom. Find fractions that are equivalent to 1 . 3 Choose a number to multiply by. Multiply the top. Multiply the bottom.

1 ×2 = 2 3 ×2 6

1 ×3 = 3 3 ×3 9

1 ×4 = 4 3 × 4 12

1 = 2 = 3 = 4 3 6 9 12

AP P LY Multiply the numerator and denominator by the same number to find an equivalent fraction. 1.

1 × 2 2 × 2=

1 × 3 2 × 3=

1 × 4 2 × 4=

1 × 5 2 × 5=

3 × 2 4 × 2=

3 × 3 4 × 3=

3 × 5 4 × 5=

3 × 10 4 × 10 =

1 × 6 10 × 6 =

10. 10 × 8 =

1 × 8

11. 10 × 10 =

1 × 10

12. 10 × 12 =

Vocabulary Equivalent fractions - two or more fractions that show the same amount

138

Level E

Numerator - the top number in a fraction Denominator - the bottom number in a fraction

| Chapter 7 - 4

| Lighthouse MATH

1 × 12

Exercise | 7 - 4 Name

Multiply the numerator and denominator by the same number to find equivalent fractions. 1.

1 × 2 2 × 2=

1 × 5 2 × 5=

2 × 4 3 × 4=

2 × 3 5 × 3=

5 × 2 6 × 2 =

4 × 2 5 × 2 =

1 × 3 6 × 3 =

3 × 4 4 × 4 =

1 × 5 3 × 5 =

10. 7 × 10 =

2 × 10

11. 8 × 2 =

3 × 2

12. 10 × 3 =

1 × 5

2 × 5

13. 4 × 5 = 20

14. 3 × 5 = 6

3 × 3

3 × 5

1 × 5

15. 4 × 5 = 12

16. 10 × 5 = 30

1 4 =

18. 5 =

19. 4 =

20. 6 =

22. 8 =

17.

21. 9 =

Find three equivalent fractions.

CH AL L ENGE Fill in the missing numbers. 1

23. 6 = 12

24. 5 = 15

Level E

| Chapter 7 - 4

25. 2 = 10

| Lighthouse MATH

26. 5 = 10

139

7 - 5 | Finding an Equivalent Fraction Solve. DAILY REV IE W

8×4=

3×4=

9×2=

3×2=

L E A R N A ND C ONNEC T The chocolate bar is divided into 12 pieces. What 2 fraction is the same as 3 of a bar?

Set up the problem.

numerator

2 3

Multiply the numerator by the same number.

Find the number you multiply the first denominator by to get the second denominator.

? 12

2 3

×4

? 12

2 3

×4

denominator

8 12

2 8 3 is equivalent to 12 .

Multiply 3 by 4 to get 12.

8 2 12 of the bar is the same as 3 of the bar.

AP P LY Find the missing factor. 1.

1 × 2 ×

= 8

1 × 5 ×

= 25

3 × 4 ×

= 8

1 × 4 ×

= 12

2 × 3 ×

= 15

3 × 4 ×

= 24

4 × 5 ×

= 15

3 × 4 ×

= 40

| Chapter 7 - 5

| Lighthouse MATH

Vocabulary Equivalent - equal in value

140

Level E

Exercise | 7 - 5 Name

Multiply the numerator and denominator by the same number to find equivalent fractions. 1.

1 2

×2 ×2 =

1 ×3 2 ×3 =

1 ×4 2 ×4 =

1 2

×5 ×5 =

3 ×2 4 ×2 =

3 ×3 4 ×3 =

3 ×5 4 ×5 =

3 × 10 4 × 10 =

Fill in the missing numerator. 9. 6 = 24

10. 3 = 21

11. 4 = 28

12. 5 = 20

13. 4 = 36

14. 2 = 18

15. 4 = 40

16. 3 = 9

17. 6 = 36

18. 5 = 35

19. 5 = 20

20. 6 = 12

22. 3 = 12

23. 5 = 20

24. 10 = 70

Read the problem. Then solve. 25. Anna’s garden is divided into 20 sections. She wants to use 35 of her garden for tomatoes. What fraction with a denominator of 20 is the same as 35 ?

26. Max is hanging a string of lights that is 15 feet long. He wants to cover 45 of the string with blue tape to mark where the bulbs go. What fraction with a denominator of 15 is 45 ?

CH AL L ENGE Find the missing numbers to make all three fractions equivalent. 2

27. 3 = 12 =

Level E

| Chapter 7 - 5

| Lighthouse MATH

141

21. 5 = 45

7 - 6 | Simplest Form Write the equivalent fraction. DAILY REV IE W

1 2 = 10

3 8 = 16

5 7 = 21

7 8 = 16

L E A R N A ND C ONNEC T We can also divide to find an equivalent fraction. This is called simplifying. A fraction is in its simplest form when you cannot divide the top and bottom by the same number (other than 1). Find the numbers that the numerator and denominator can be divided by.

6 8

Divide the numerator and denominator by the same number. 6 ÷2= 3 8 ÷2= 4

can be divided by: 1, 2, 3, 6 can be divided by: 1, 2, 4, 8

Both can be divided by 2. So, 6 is not in simplest form. 8

AP P LY Divide the numerator and denominator by the same number to put the fraction in simplest form. 1.

6 ÷3 9 ÷3 =

8 ÷4 12 ÷ 4 =

15 ÷ 5 25 ÷ 5 =

18 ÷ 6 24 ÷ 6 =

21 ÷ 7 49 ÷ 7 =

30 ÷ 10 50 ÷ 10 =

36 ÷ 12 48 ÷ 12 =

7 ÷7 21 ÷ 7 =

50 ÷ 10 60 ÷ 10 =

10. 8 ÷ 4 =

4 ÷4

11. 100 ÷ 25 =

25 ÷ 25

12. 16 ÷ 4 =

Vocabulary Simplest form - a fraction where the numerator and denominator cannot be divided by the same number other than 1

142

Level E

| Chapter 7 - 6

| Lighthouse MATH

4 ÷4

Exercise | 7 - 6 Name

Look at each student’s work. Is their fraction in simplest form? Write Yes or No. 12 ÷ 4

Nick’s work: 40 ÷ 4 = 10 3

16 ÷ 2

Is 8 in simplest form?

Harry’s work: 40 ÷ 2 = 20 8

70 ÷ 10

Is 8 in simplest form?

Write each fraction in simplest form. 5.

George’s work: 80 ÷ 10 = 8 7

Is 20 in simplest form?

4 = 8 =

Is 10 in simplest form?

36 ÷ 9

Solomon’s work: 72 ÷ 9 = 8

Tip!

6 = 9 =

12 = 16 =

14 = 21 =

10. 20 =

11. 30 =

20 =

12. 20 =

8 =

13. 30 =

18 =

14. 32 =

24 =

15. 27 =

16. 100 =

10 =

17. 10 =

4 =

18. 18 =

6 =

19. 15 =

9 =

20. 20 =

14 =

22. 24 =

16 =

23. 45 =

15 =

24. 28 =

21 =

25. 25 =

21. 28 =

10 = 15 =

If your answer is not in simplest form, you can divide again. 4 ÷2= 2 8 ÷2= 4

15 =

2 ÷2= 1 4 ÷2= 2

9 =

12 =

20 =

CH AL L ENGE Simplify the two fractions to see if they are equivalent. 24

26. 36 and 90

Level E

| Chapter 7 - 6

| Lighthouse MATH

143

7 - 7 | Common Denominators Simplify. DAILY REV IE W

6 10 =

9 12 =

10 20 =

12 18 =

L E A R N A ND C ONNEC T If two fractions do not have the same denominator, we can find equivalent fractions that have a common denominator. 1 1 and 2 5 Find a number both denominators can become. Tip: You can multiply the denominators together.

Multiply. Whatever you do to the bottom, do to the top.

1 2

2 × 5 = 10

1 ×5= 5 2 × 5 = 10

1 5

5 × 2 = 10

1 ×2= 2 5 × 2 = 10

AP P LY Rewrite one or both fractions to have a common denominator. 1.

1 2 3, 5

1 3 5 , 10

Tip! Sometimes only one fraction needs to be changed!

1 5 6, 8

1 and 1 4 2

3 5 4 , 12

1 ×2 = 2 2 ×2 4

Vocabulary Common denominator - when the denominators of two or more fractions are the same

144

Level E

| Chapter 7 - 7

| Lighthouse MATH

Exercise | 7 - 7 Name

Find equivalent fractions with a common denominator. 1 1 2, 8

1 1 3, 6

2 3 5 , 10

1 3 4, 8

3 1 4, 5

1 1 5, 2

1 2 10 , 5

1 3 2 , 10

10. 3 , 4

12. 8 , 4

13. 4 , 6

14. 9 , 2

15. 8 , 16

17.

1 2 9, 3

18. 7 , 2

19. 12 , 3

20. 5 , 4

22. 5 , 3

23. 9 , 2

24. 10 , 5

25. 3 , 11

11. 6 , 4

16. 7 , 3

21. 6 , 12

1 1 2, 3

Read the problem. Then solve. 7 of an inch long. 26. A ribbon is 10 The teacher cut 25 of an inch off of the ribbon. Rewrite the fractions to have the same denominator.

27. A fish bowl has 83 of a gallon of water. Tim took 61 of a gallon of the water out. Rewrite the fractions to have the same denominator.

CH AL L ENGE Rewrite all the fractions so that they have the same denominator. 1

28. 2 , 4 , 5 , 10

Level E

| Chapter 7 - 7

| Lighthouse MATH

145

7 - 8 | Comparing and Ordering Fractions Find equivalent fractions with a common denominator. 1.

DAILY REV IE W

1 1 5 and 4

2 5 3 and 6

3 3 4 and 10

1 1 7 and 2

L E A R N A ND C ONNEC T 7 8

We can compare fractions if they have the same denominator. If they don't, we can write new fractions with a common denominator. 2

Compare 3 and 8 .

2 3

Write > for greater than. Write < for less than.

Find equivalent fractions with a common denominator.

Compare the numerators.

2 × 8 = 16 3 × 8 24

16 24

7 × 3 = 21 8 × 3 24

21 24

Write the original fractions with < or >. 2 3

7 8

16 is less than 21.

AP P LY Find equivalent fractions. Compare the numbers. Fill in > or <. 1.

1 2 2 and 3

1 2 = 6

2 1 3 = 6 2

2 3

1 1 3 and 4

1 3 = 12

1 1 4 = 12 3

1 4

5 1 8 and 2

5 8

1 5 2 = 8 8

1 2

146

Level E

| Chapter 7 - 8

| Lighthouse MATH

Exercise | 7 - 8 Name

Write > or < to compare the fractions. 1. 4

3 4

2. 10

2 4

3. 10

5 6

4. 3

5 6

5. 2

2 5

6. 5

2 6

7. 10

3 5

8. 4

2 3

9. 9

1 8

10. 6

2 6

11. 6

1 2

12. 4

4 5

13. 6

3 8

14. 4

4 7

15. 4

3 9

16. 7

1 3

4 6

18. 8

1 2

19. 7

1 3

20. 5

4 8

17. 9

21. One screw is 43 of an inch thick. Another screw is 21 an inch thick. Which screw is thicker?

Read the problem. Then solve. 9 of a mile toward the 22. Rose walked 10 park. Sara walked 32 of a mile. Who is closer to the park?

CH AL L ENGE Order these fractions from least to greatest. 2

23. 25 , 20, 9 , 100

Level E

| Chapter 7 - 8

| Lighthouse MATH

147

7 - 9 | Improper Fractions Write > for greater than. Write < for less than. DAILY REV IE W

2 3

3 5

1 4

3 8

5 6

4 5

7 10

3 4

L E A R N A ND C ONNEC T An improper fraction has a numerator that is greater than or equal to the denominator. Improper fractions are greater than or equal to 1. Each slice is 1 of the pizza. 8 There are 20 slices. There are 20 of pizza. 8

AP P LY Write an improper fraction for each picture.

2. 4

4. 8

6. 5

Vocabulary Improper fraction - a fraction where the numerator is greater than the denominator; a fraction greater than one

148

Level E

Numerator - the top number in a fraction Denominator - the bottom number in a fraction

| Chapter 7 - 9

| Lighthouse MATH

Exercise | 7 - 9 Name

Write an improper fraction for each picture. 1.

Draw a picture to show each improper fraction. 7 3

8 5

9 2

5 4

10 6

10. 7

CH AL L ENGE 11. A bakery cuts its cakes into fourths and sells them by the slice. If you want 2 whole cakes and 1 extra slice, what fraction of cake do you need to buy?

Level E

| Chapter 7 - 9

| Lighthouse MATH

149

7 - 10 | Mixed Numbers Draw a picture to show each improper fraction. DAILY REV IE W

6 4

21 9

L E A R N A ND C ONNEC T Improper fractions can be written as mixed numbers. A mixed number tells the number of wholes, and the extra is written as a fraction part.

There are 2 whole cookies. 2 There is an extra of a cookie. 3 2 There are 2 cookies. 3 We can write the number of cookies in two ways:

8 Improper fraction: 3

2 Mixed number: 2 3

AP P LY Write a mixed number for each picture. 1.

Vocabulary Mixed number - a whole number with an extra fraction part Improper fraction - a fraction where the numerator is greater than the denominator; a fraction greater than one Numerator - the top number in a fraction Denominator - the bottom number in a fraction

150

Level E

| Chapter 7 - 10

| Lighthouse MATH

Exercise | 7 - 10 Name

Draw a picture of the improper fraction. Write the equivalent mixed number. Improper fraction

7 4

11 6

32 10

14 3

Drawing

Mixed number

Draw a picture of the mixed number. Write the equivalent improper fraction. Mixed number

Drawing

Improper fraction

CH AL L ENGE 9. Sara is putting away blocks on the shelves. She has 20 blocks, and each shelf holds 6 blocks. How many shelves will the blocks take up? Write the answer as a mixed number.

Level E

| Chapter 7 - 10

| Lighthouse MATH

151

7 - 11 | Converting Improper Fractions to Mixed Numbers Color the improper fraction or mixed number. 1.

DAILY REV IE W

5 2

3 3

L E A R N A ND C ONNEC T We can change an improper fraction to a mixed number.

8 8

Divide the numerator by the denominator. 19 8

2R3 8 19 − 16 3

Improper fraction

3 8

Change the remainder into a fraction by writing it over the divisor. 3 2 8 8 19 − 16 3

28 Mixed number

AP P LY Divide the numerator by the denominator to make a mixed number. 1.

7 6

6 7 −

2. 6

5 3

3 5 −

3. 3

16 5

5 1 6 −

4. 5

Vocabulary Improper fraction - a fraction that has a numerator equal to or larger than the denominator

152

Level E

| Chapter 7 - 11

| Lighthouse MATH

11 4

4 1 1 −

Exercise | 7 - 11 Name

Draw a picture of the improper fraction. Write the equivalent mixed number. Improper fraction

Drawing

Mixed number

7 4

11 6

32 10

14 3

Write as a mixed number. 5 3

10 9

11.

8 7

12. 3

10. 2

14 5

10 3

13. 3

8 3

14. 6

CH AL L ENGE Simplify. Then write as a mixed number. 15.

150 36

Level E

| Chapter 7 - 11

| Lighthouse MATH

153

7 - 12 | Converting Mixed Numbers to Improper Fractions Write the improper fraction as a mixed number. DAILY REV IE W

17 5

22 9

31 6

13 4

L E A R N A ND C ONNEC T To change a mixed number to an improper fraction, we can use the MAD method.

Mixed number

M Multiply

A Add

D Denominator

Multiply the whole number by the denominator.

Add the numerator.

Write it as a fraction over the same denominator.

3 × 5 = 15

15 + 4 = 19

19/5

19 5 Improper fraction

AP P LY Draw a picture of the mixed number. Write the equivalent improper fraction. Mixed number

Drawing

Vocabulary Mixed number - a number that has both whole and fraction parts

154

Level E

| Chapter 7 - 12

| Lighthouse MATH

Improper fraction

Exercise | 7 - 12 Name

Write each number as an improper fraction. 2. 3 5 =

12. 8 2 =

17. 4 4 =

22. 2 2 =

27. 3 5 =

6. 4 4 =

11. 5 3 =

16. 8 10 =

21. 8 5 =

26. 2 3 =

3. 8 4 =

4. 6 5 =

95 =

8. 4 5 =

13. 4 2 =

18. 9 2 =

23. 4 3 =

28. 1 8 =

5. 5 10 =

9. 2 5 =

14. 5 10 =

19. 6 4 =

24. 5 2 =

29. 4 4 =

10. 4 3 =

15. 2 5 =

20. 3 5 =

25. 4 2 =

30. 5 2 =

1. 7 3 =

CH AL L ENGE Write each mixed number as an improper fraction. 1

31. 17 4 =

32. 21 3 =

Level E

| Chapter 7 - 12

| Lighthouse MATH

155

7 - 13 | Chapter Review Write each mixed number as an improper fraction. DAILY REV IE W

3 10

L E T ' S REV I EW Writing Fractions

Finding Equivalent Fractions

Look for the total number of equal parts and number of parts shaded.

Multiply or divide the numerator and denominator by the same number.

6 parts out of 8 are shaded in this circle. 6 8

Numerator

Denominator

3 is written in simplest form. 4

Comparing Fractions

Improper Fractions and Mixed Numbers

Find fractions with a common denominator. Compare the numerators.

2 3 8 8 19 − 16 3

3 4 © Lighthouse Curriculum. Copying strictly prohibited.

6 ÷2 3 = 8 ÷2 4

19 8

1 3

3 ×3 9 = 4 × 3 12

Improper fraction

1 ×4 4 = 3 × 4 12

9 is greater than 4 so

Long division

Mixed number

2 8

2 × 8 = 16 16 + 3 = 19

19 8

Mixed number

MAD method

Improper fraction

3 1 > 4 3

2 83

AP P LY Fill in the missing numerator. 1.

2 7 = 7

1 7 = 63

2 4 = 8

1 7 = 49

2 3 = 15

1 7 = 35

4 4 = 8

3 10 = 70

156

Level E

| Chapter 7 - 13

| Lighthouse MATH

Exercise | 7 - 13 Name

Write each fraction in simplest form. 1. 20 =

2. 16 =

3. 24 =

4. 25 =

5. 30 =

6. 28 =

8. 22 =

9. 42 =

10. 30 =

11. 32 =

12. 36 =

7. 36 =

Compare the fractions using >, <, or =. 13. 8

2 3

14. 6

4 5

15. 4

2 8

16. 7

4 6

17. 9

5 12

3 8

19. 10

2 5

20. 4

3 5

21. 7

4 6

22. 9

2 10

18. 16

Write each improper fraction as a mixed number in simplest form. 23. 8

24. 12

25. 4

26. 12

27. 24

29. 16

30. 4

31. 15

32. 36

36. 6 8

37. 4 5

42. 9 7

28. 20

Write each mixed number as an improper fraction. 33. 4 8

34. 1 7

35. 3 9

39. 3 7

40. 10 5

41. 4 15

| Chapter 7 - 13

| Lighthouse MATH

38. 14 3

Level E

157

7 - 14 | Cumulative Review

Solve. 1.

1 × 3

3 + 5

13 − 6

8 × 7

6 + 5

14 − 9

3 × 6

1 × 6

1 + 5

10.

8 − 6

11.

2 + 1

12.

9 − 1

13.

4 + 7

14.

5 + 2

15.

8 × 9

16.

7 − 5

17.

9 − 6

18.

11 − 9

19.

4 × 8

20.

3 × 9

21.

5 + 4

22.

7 + 8

23.

3 × 8

24.

4 + 5

25.

5 × 1

26.

5 − 1

27.

10 − 7

28.

3 + 4

29.

6 × 2

30.

14 − 6

31.

6 − 3

32.

5 + 5

33.

2 − 1

34.

9 − 8

35.

6 + 6

36.

17 − 8

37. 1 3

38. 2 10

39. 3 15

40. 8 56

41. 3 21

42. 5 20

43. 2 18

44. 2 12

45. 4 24

46. 6 30

47. 3 6

48. 3 12

49. 9 18

50. 3 3

51. 2 6

52. 6 48

53. 1 6

54. 1 9

158

Level E

| Chapter 7 - 14

| Lighthouse MATH

Exercise | 7 - 14 Name

Add. 1.

465 + 248

306 + 703

837 + 586

4,676 + 7,716

3,221 + 1,413

507 − 371

525 − 404

4,047 − 2,560

10.

4,516 − 536

12.

677 × 6

13.

1,930 × 7

14.

1,454 × 7

15.

95 × 92

Subtract. 6.

622 − 297

Multiply. 11.

128 × 6

16. 7 392

17. 4 167

18. 6 4,356

19. 8 2,832

20. 65 3,120

23. 16,359

24. 109,836

25. 248,367

28. 409,239

29. 87,999

30. 319,845

Divide.

Round to the nearest hundred. 21. 398

22. 5,639

Round to the nearest thousand. 26. 5,692

27. 38,284

Level E

| Chapter 7 - 14

| Lighthouse MATH

159

8 C H A P T E R

160

In Chapter 8, we will learn about

Adding and Subtracting Fractions Fractions can be added and subtracted. To add or subtract fractions, the fractions must have the same denominator. • We will practice adding and subtracting fractions with the same denominator. • We will find equivalent fractions with common denominators so that we can add and subtract fractions. • We will add and subtract mixed numbers. • We will subtract a fraction from a whole number.

161

8 - 1 | Adding Fractions with Like Denominators Write the fraction in simplest form. DAILY REV IE W

3 9

2 4

3 15

2 8

L E A R N A ND C ONNEC T When fractions have the same denominator, we can add the numerators and keep the denominator. Paul ate 81 of a pizza, and Aaron ate 83 of the pizza. How much pizza did they eat in total? To find the total amount of pizza, add

Add the numerators.

Keep the denominator the same.

Simplify.

1 + 3 = 4 8 8

1 + 3 = 4 8 8 8

4 ÷4 = 1 8 ÷4 2

Paul and Aaron ate 2 of a pizza.

AP P LY Add. Write your answer in simplest form. 1. 5 + 5

2. 9 + 9

3. 11 + 11

4. 5 + 5

5. 8 + 8

7. 6 + 6

8. 8 + 8

9. 12 + 12

10. 4 + 4

6. 9 + 9

Vocabulary Numerator - the top number that shows how many parts of the whole Denominator - the bottom number below the fraction bar that shows how many equal parts make the whole Simplest form - when the numerator and denominator do not share any factors except for 1

162

Level E

| Chapter 8 - 1

| Lighthouse MATH

Exercise | 8 - 1 Name

1. 3 + 3

2. 8 + 8

3. 9 + 9

4. 5 + 5

5. 10 + 10

6. 5 + 5

7. 9 + 9

8. 5 + 5

9. 15 + 15

10. 7 + 7

11. 5 + 5

12. 10 + 10

13. 14 + 14

14. 8 + 8

15. 9 + 9

16. 11 + 11

17. 7 + 7

18. 9 + 9

19. 6 + 6

20. 5 + 5

22. 12 + 12

23. 9 + 9

24. 9 + 9

25. 14 + 14

21. 13 + 13

Read the problem. Then solve. 26. Sara planted 37 of the garden, and Ann planted 27 of the garden. How much of the garden did they plant altogether?

27. On Tuesday, it rained 81 of an inch, and on Wednesday, it rained 83 of an inch. What was the total rainfall?

CH AL L ENGE Fill in the missing fraction. 3

28. 4 +

29. 10 +

Level E

= 10

30. 3 +

| Chapter 8 - 1

| Lighthouse MATH

=13

31. 8 +

=14

163

Add. Simplify.

8 - 2 | Subtracting Fractions with Like Denominators Solve. DAILY REV IE W

1 2 5 + 5 =

3 1 8 + 8 =

7 1 10 + 10 =

1 4 6 + 6 =

L E A R N A ND C ONNEC T When fractions have the same denominator, we can subtract the numerators and keep the denominator. Mike has 97 of a bar of chocolate. He gives away 4 9 of the bar. How much of the chocolate bar does he have left? To find the amount left, subtract

−

Subtract the numerators.

Keep the denominator the same.

Simplify.

7 − 4 = 3 9 9

7 − 4 = 3 9 9 9

3 ÷3 = 1 9 ÷3 3

There is 3 of the chocolate bar left.

AP P LY Subtract. Write your answer in simplest form. 1. 4 − 4

2. 9 − 9

3. 6 − 6

4. 7 − 7

5. 5 − 5

7. 4 − 4

8. 3 − 3

9. 5 − 5

10. 2 − 2

6. 3 − 3

164

Level E

| Chapter 8 - 2

| Lighthouse MATH

Exercise | 8 - 2 Name

1. 5 − 5

2. 4 − 4

3. 8 − 8

4. 11 − 11

5. 9 − 9

6. 8 − 8

7. 9 − 9

8. 8 − 8

9. 10 − 10

10. 15 − 15

11. 12 − 12

12. 13 − 13

13. 8 − 8

14. 5 − 5

15. 14 − 14

16. 4 − 4

17. 3 − 3

18. 7 − 7

19. 8 − 8

20. 3 − 3

22. 9 − 9

23. 3 − 3

24. 13 − 13

25. 7 − 7

21. 6 − 6

Read the problem. Then solve. 7 26. A ribbon is 10 inches long. The teacher 3 cut 10 inches off of the ribbon. How much is left?

27. A fish bowl has 65 gallons of water. Tim took 61 gallons of the water out. How many gallons are in the fish bowl now?

CH AL L ENGE Find the missing fraction. 5

28. 9 −

= 9

29. 9 −

Level E

= 3

30. 15 −

| Chapter 8 - 2

| Lighthouse MATH

= 5

31. 12 −

= 2

165

Subtract. Reduce to simplest form.

8 - 3 | Adding Fractions with Unlike Denominators Solve. DAILY REV IE W

2 1 3 − 3 =

4 2 5 − 5 =

5 2 8 − 8 =

3 1 10 − 10 =

L E A R N A ND C ONNEC T When fractions have different denominators, we need to find equivalent fractions with a common denominator before we can add. Add 41 + 31 . Rewrite the fractions with a common denominator. 1 ×3 = 3 4 × 3 12

Add the numerators. Keep the denominators the same.

Simplify if needed.

3 + 4 = 7 12 12 12

7 is in the 12 simplest form.

1 ×4 = 4 3 × 4 12

AP P LY

Add. 1

1. 2 + 3 6 + 6 = 6 2

166

+ 1

Level E

6. 3 + 9

8. 8 + 2 =

8 + 8 = 8

5. 5 + 6

7. 5 + 3 +

3. 2 + 8

20 + 20 = 20 2

4. 3 + 6 +

2. 5 + 4

= 1

9. 4 + 6 =

| Chapter 8 - 3

| Lighthouse MATH

Exercise | 8 - 3 Name

1. 2 + 5 =

2. 3 + 4 =

3. 5 + 2 =

4. 8 + 4 =

5. 10 + 5 =

6. 9 + 3 =

7. 6 + 2 =

8. 5 + 10 =

9. 4 + 12 =

10. 8 + 2 =

11. 9 + 2 =

12. 12 + 3 =

13. 7 + 3 =

14. 4 + 5 =

15. 10 + 4 =

16. 8 + 6 =

17. 2 + 7 =

18. 6 + 4 =

19. 7 + 2 =

20. 4 + 10 =

22. 3 + 4 =

23. 5 + 6 =

24. 12 + 3 =

21. 6 + 3 =

Add.

CH AL L ENGE Find the missing numerator. 3

25. 5 + 6 = 30

26. 7 + 5 = 35

Level E

| Chapter 8 - 3

| Lighthouse MATH

167

8 - 4 | Subtracting Fractions with Unlike Denominators Solve. DAILY REV IE W

1 2 4 + 3 =

3 1 10 + 2 =

1 3 6 + 5 =

5 1 8 + 4 =

L E A R N A ND C ONNEC T David has a piece of wood that is 43 of a foot long. He cuts off 85 of a foot. What is the length of the leftover piece? To find the length left over, subtract from

. Subtract the numerators. Keep the denominators the same.

Rewrite the fractions with a common denominator. 3 ×2 = 6 4 ×2 8

5 8

Simplify if needed.

6 − 5 = 1 8 8 8

1 8

is in the simplest form.

The leftover piece is 8 of a foot long.

AP P LY Subtract. 3

1. 4 − 3 9 12 − 12 = 12 7

168

18 − 18 = 18

5. 12 − 6 =

−

Level E

3. 9 − 2

6 − 6 = 6 7

4. 8 − 4 −

2. 6 − 3

6. 7 − 3 =

| Chapter 8 - 4

−

| Lighthouse MATH

Exercise | 8 - 4 Name

1. 2 − 4 =

2. 3 − 6 =

3. 4 − 3 =

4. 5 − 2 =

5. 8 − 4 =

6. 10 − 5 =

7. 3 − 5 =

8. 12 − 4 =

9. 4 − 8 =

10. 7 − 3 =

11. 2 − 10 =

12. 9 − 3 =

13. 8 − 2 =

14. 5 − 4 =

15. 4 − 10 =

16. 6 − 8 =

17. 10 − 4 =

18. 3 − 9 =

19. 7 − 2 =

20. 12 − 4 =

22. 3 − 5 =

23. 12 − 2 =

24. 2 − 7 =

21. 6 − 3 =

Subtract.

CH AL L ENGE Find the missing numerator. 5

25. 6 − 4 − 3 = 4

Level E

| Chapter 8 - 4

| Lighthouse MATH

169

8 - 5 | Adding Mixed Numbers Solve. DAILY REV IE W

3 1 4 − 6 =

4 1 5 − 2 =

5 1 8 − 3 =

2 2 3 − 9 =

L E A R N A ND C ONNEC T When adding mixed numbers, first add the fraction parts, then add the whole numbers. Add 2 21 and 1 41 . Rewrite the fractions with a common denominator.

Add the fraction parts.

Add the whole numbers.

2 42

1 + 1 4

3 4

3 43

2 21 = 2 42 1 41 = 1 41

Simplify if needed.

in the 3 43 is simplest form.

AP P LY Add. 1.

13 1

+ 2 2

35 1

+ 1 4

+ 3 5

170

24 1

+ 1 2

1 1

+ 4 9

Level E

| Chapter 8 - 5

13 +

| Lighthouse MATH

24 1

+ 5 6

Exercise | 8 - 5 Name

Add. Write your answers in simplest form. 3

4 10

19 1

12.

23 1

+ 3 4

17.

45 1

+ 2 3

10.

15.

19.

25 2

+ 6 2

+ 4 10

48 1

+ 1 2

1 10

23 + 5 7

+ 5 10

18.

14.

26 6

+ 4 5

+ 2 4

13.

420

28 + 4 6

+ 1 3

+ 2 3

16.

87 1

+ 3 2

+ 2 6

59 1

+ 1 4

+ 2 3

11.

3 12 1

+ 2 5

+ 3 5

+ 2 3

20.

36 1

+ 2 4

21. Ben is making a snack mix for a trip. He mixes together 2 31 cups of peanuts and 2 21 cups of raisins. What is the total amount of snack mix?

22. Paul is building a fence around his garden. He finishes 4 81 yards of the fence Monday and 3 41 yards the next day. How many total yards of fencing is completed?

CH AL L ENGE Solve. 1

23. 1 2 +1 2 =

24. 3 2 + 1 4 =

Level E

| Chapter 8 - 5

| Lighthouse MATH

171

Read the problem. Then solve.

8 - 6 | Subtracting Mixed Numbers Solve. DAILY REV IE W

23 +3 2 =

43 +19 =

18 +54 =

36 +2 5 =

L E A R N A ND C ONNEC T Anna has 5 43 cups of orange juice. She uses 2 31 cups of it. How many cups of juice are left? We need to subtract

from

Rewrite the fractions with a common denominator. 9 5 43 = 5 12

Subtract the fraction parts.

Subtract the whole numbers. Simplify if needed.

9 5 12

− 2

4 2 31 = 2 12

4 12

− 2

5 12

4 12

5 3 12

Anna has 3 12 cups of orange juice left.

AP P LY Subtract. 1.

44 1

− 1 2

−

63 2

− 3 5

−

− 4 3

172

55 1

− 2 4

−

7 1

−

− 1 3

Level E

| Chapter 8 - 6

48 −

| Lighthouse MATH

63 1

− 2 4

−

Exercise | 8 - 6 Name

Subtract. Write your answer in simplest form. 1

88 1

67 1

85 1

− 4 4

64 3

− 2 10

56 3

− 1 8

10 12

10.

14.

4 12

15.

10 2 1

− 5 7

44 − 1 8

98 1

− 1 2

19.

36 − 1 3

− 4 4

− 2 3

18.

− 1 10

17.

13.

− 2 5

− 3 3

16.

74 − 2 3

− 5 5

12.

− 3 2

− 4 4

11.

9 10

65 1

− 1 6

− 2 4

− 3 2

20.

7 10 1

− 3 4

21. A gardener has a piece of wood that is 7 810 feet long. He needs to cut off a piece that is 3 25 feet long. How long will the remaining piece of wood be?

22. There are 6 43 liters of punch in a pitcher in the morning. After lunch, the pitcher has only 2 61 liters. How much punch was drunk?

CH AL L ENGE Solve. 1

23. 4 3 −1 2 =

Level E

| Chapter 8 - 6

| Lighthouse MATH

173

Read the problem. Then solve.

8 - 7 | Subtracting from a Whole Number Solve. 1.

DAILY REV IE W

75 1

− 2 2

66 1

− 4 3

88 3

− 3 4

43 1

− 5 4

− 1 5

L E A R N A ND C ONNEC T When subtracting a fraction from a whole number, first change the whole number to a mixed number.

Remember: the same numerator with Fractions r are equal to 1. nato omi and den 10 1 = 10

Rewrite one whole as a fraction with the same numerator and denominator. 3 Subtract 4 − 2 10 .

Rewrite the whole number.

Subtract the fraction parts.

Subtract the whole numbers. Simplify if needed.

4 = 3 + 1 4 = 3 + 10 10

3 10 10

− 2

4 = 3 10 10

3 10

− 2

3 10

7 1 10

7 10

AP P LY Rewrite each whole number as a mixed number. 1. 5=4 7 5. 6= 9. 10 =

174

2. 8=7 5

3. 9=86

4. 4=3 7

6. 4=

7. 5=

8. 3=

10. 7=

11. 6=

12. 9=

| Chapter 8 - 7

| Lighthouse MATH

Level E

Exercise | 8 - 7 Name

Subtract. Simplify if needed. 1.

4 1

− 1 3

− 6 9

11.

12.

12 7

− 3 10

16.

17.

13 1

− 6 2

− 2 5

14.

15.

19. 5

− 3 7

− 2 7

20.

5 − 1 8

5 4

− 3 6

20 − 10 4

− 1 12

18.

10.

4 − 2 10

− 8 3

− 1 4

− 4 8

13.

6 3

− 4 6

− 1 5

9 5

− 3 8

5 1

− 2 5

10 2

− 4 9

21. A climber has a rope that is 15 feet long. She cuts off a piece that is 6 83 feet long. How much rope does she have left?

Read the problem. Then solve. 22. Mrs. Davis has 5 cups of orange juice in a pitcher. She uses 2 45 cups to make a batch of punch. How many cups of orange juice remain in the pitcher?

CH AL L ENGE Solve. 1

23. 74 −24 =

24. 3 2 − 1 5 =

Level E

| Chapter 8 - 7

| Lighthouse MATH

175

8 - 8 | Chapter Review Solve. 1.

5 3

DAILY REV IE W

8 1

− 2 4

7 2

− 4 3

7 5

− 3 5

6 7

− 2 7

− 1 10

L E T ' S REV I EW Fractions with

Fractions with

Subtracting from a

Like Denominators

Unlike Denominators

Whole Number

Add or subtract the numerators. Simplify if needed.

Multiply one or both fractions to get common denominators before adding or subtracting.

Rewrite the whole number as a mixed number. Remember, a fraction with the same numerator and denominator is equal to 1 whole.

2 + 3 = 5 7 7 7 7 − 3 = 4 = 2 10 10 10 5

−

5 × 4 = 9 4 1 × 3 = − 12 3

20 36 3 36

5 − 2

5 6

− 2

17 36

5 6 1

AP P LY Add. 1 3

1. +

1 3

56 1

+ 5 6

176

3 10

2. +

4 10

44 2

+ 2 4

Level E

5 9

3. +

3 9

5 10 1

+ 1 10

| Chapter 8 - 8

4 10

4. +

5 10

38 1

+ 2 8

| Lighthouse MATH

1 3

5. +

10.

1 3

15 1

+ 5 5

Exercise | 8 - 8 Name

Subtract. 3 10

1 10

−

4 6

3 6

−

4 10

1 5

−

10.

− 1 4

4 5

1 4

−

− 1 10

2 4

1 3

−

− 1 5

2 3

33 1

− 1 6

− 2 3

Write each pair of fractions with common denominators. 1

11. 3 , 4

12. 5 , 6

13. 8 , 2

14. 9 , 3

15. 6 , 8

16.

17.

24 1

− 3 2

18.

3 10 3

+ 1 3

19.

20.

+ 1 4

Solve. 1

53 1

+ 1 3

− 1 6

Subtract. 21.

22.

4 1

− 1 5

23.

8 1

− 2 3

Level E

24.

6 3

− 1 4

| Chapter 8 - 8

25.

3 5

− 1 8

| Lighthouse MATH

5 5

− 2 6

177

8 - 9 | Cumulative Review

Solve. 1.

17 − 9

11 − 5

3 + 4

4 × 4

6 × 8

9 × 6

8 + 6

8 − 5

7 + 2

10.

11 − 2

11.

5 × 7

12.

3 × 9

13.

2 + 5

14.

8 + 4

15.

7 × 8

16.

6 + 3

17.

10 − 4

18.

2 × 5

19.

2 + 3

20.

5 × 4

21.

2 + 8

22.

3 − 1

23.

3 × 4

24.

4 × 3

25.

1 + 2

26.

1 + 3

27.

16 − 8

28.

2 × 8

29.

14 − 9

30.

3 + 1

31.

12 − 3

32.

10 − 9

33.

6 × 1

34.

5 + 9

35.

8 × 8

36.

4 × 2

37. 7 7

38. 6 36

39. 5 40

40. 8 56

41. 1 6

42. 9 45

43. 3 27

44. 9 72

45. 7 56

46. 1 9

47. 2 6

48. 1 3

49. 7 14

50. 3 21

51. 3 12

52. 1 5

53. 4 4

54. 4 8

178

Level E

| Chapter 8 - 9

| Lighthouse MATH

Exercise | 8 - 9 Name

Add. 1.

780 + 616

384 + 349

193 + 786

7,776 + 1,307

9,010 + 5,990

844 − 588

683 − 14

7,999 − 2,538

10.

7,574 − 1,944

12.

195 × 3

13.

4,491 × 2

14.

5,838 × 7

15.

63 × 67

Subtract. 6.

870 − 795

Multiply. 11.

420 × 8

Divide. 17. 8 304

18. 3 216

19. 5 1,857

20. 2 315

16. 3 187

Solve and write “round it,” “use it,” or “drop it” next to the problem. 21. Moses puts 38 apples into bags that hold 6 apples each. How many full bags can he make?

22. The teacher lines up 34 students in rows of 5 for an activity. How many students are left over?

23. Paul buys 26 cards. Each booklet holds 4 cards. How many booklets does he need?

24. Sara plants 47 flowers in rows of 7. How many full rows can she plant?

Level E

| Chapter 8 - 9

| Lighthouse MATH

179

9 C H A P T E R

180

In Chapter 9, we will learn about

Multiplying and Dividing Fractions We can multiply and divide fractions without finding a common denominator. Follow simple steps to find the product or quotient. • We will multiply fractions. • We will cross simplify fractions before multiplying to make multiplying easier. • We will learn about reciprocals. • We will use reciprocals to divide fractions.

181

9 - 1 | Multiplying Fractions Solve. 1. DAILY REV IE W

38 1

+ 1 4

− 4 10

− 3 4

+ 4 4

− 2 5

L E A R N A ND C ONNEC T To multiply fractions, multiply straight across the top and straight across the bottom. Multiply the numerators. Multiply the denominators. Simplify if needed.

To multiply a fraction by a whole number, use a denominator of 1. Then, multiply the numerators and denominators and simplify.

1 × 2 = 2 = 1 2 3 6 3

1 ×2 3

1 × 2 = 2 3 1 3

AP P LY Multiply. Write your answer in simplest form. 1. 2 × 3

2. 8 × 2

3. 7 × 3

4. 9 × 5

5. 7 × 6

6. 8 ×9

7. 4 ×5

8. 6 ×6

9. 7 ×3

10. 3 × 6

182

Level E

| Chapter 9 - 1

| Lighthouse MATH

Exercise | 9 - 1 Name

Multiply. Write your answer in simplest form. 1. 2 × 7

2. 8× 5

6. 3 ×3

7. 24 × 4

8. 4 × 16

9. 9× 6

10. 5 × 4

11. 3 × 12

12. 5 × 2

13. 4 × 9

14. 8 × 8

15. 3 × 3

16. 6 × 14

17. 3 × 6

18. 8 × 10

19. 12 × 3

20. 4 × 5

21. 3 × 6

22. 9 × 3

23. 3 × 12

24. 5 × 3

25. 5 × 3

3. 5 × 35

4. 7 × 42

5. 8 × 3

Read the problem. Then solve. Simplify if needed. 26. There is 32 of a cake left. Rebecca ate 45 of it. How much of the whole cake did Rebecca eat?

27. 35 of the walls are white. Jeff plans to decorate 65 of the white walls. What fraction of the walls will be decorated?

CH AL L ENGE Solve. 28. Morris wants to make 41 of his recipe. If the original recipe asked for 2 21 cups of sugar, how much sugar will the new recipe need? Level E

| Chapter 9 - 1

| Lighthouse MATH

183

9 - 2 | Cross Simplification Multiply. Write your answer in simplest form. 3

1. 8 × 6

DAILY REV IE W

2. 12 × 10

3. 7 × 8

4. 12 × 3

L E A R N A ND C ONNEC T When multiplying fractions, numbers can get large. We can divide on the diagonals to simplify before multiplying. This is called cross simplification. 3

Multiply 8 × 9 . Look at the diagonals. Can each set be divided by the same number?

Divide each set of numbers. 3÷3=1

3 8

4 9

3 and 9 can both be divided by 3. 4 and 8 can both be divided by 4.

Write the new fractions. Multiply the numerators. Multiply the denominators.

4÷4=1 3 8

4 9

8÷4=2

1 × 1 = 1 2 3 6 9÷3=3

AP P LY Use cross simplification to write new fractions. Then, multiply. 1

1. 4 × 12

1 12 1 × 1 = 4 × 1 = 2

4. 3 × 15

2. 5 × 9

2 10 5 × 14 =

Cross simplification - simplifying diagonally before multiplying

Level E

| Chapter 9 - 2

6. 9 × 24

Vocabulary

184

2 4 8 × 10 = 8

5. 5 × 14

2 15 2 × 1 = 3 × 1 =

3. 8 × 10

3 1 1 = 5 × 9 = 5 ×

| Lighthouse MATH

5. 16 × 4

8 18 9 × 24 =

Exercise | 9 - 2 Name

Multiply. Write your answer in simplest form. 1. 3 × 24

2. 5 × 7

3. 5 × 12

4. 5 × 24

5. 7 × 28

6. 9 × 63

7. 3 × 15

8. 12 × 6

9. 9 × 6

10. 7 × 15

11. 4 × 12

12. 7 × 49

13. 5 × 45

14. 9 × 72

15. 11 × 36

16. 2 × 18

17. 3 × 16

18. 3 × 4

19. 8 × 15

20. 4 × 9

21. Jeffrey is walking on a trail that is 41 of a 8 mile long. He walks 10 of the trail before stopping. How many miles did he walk?

22. A farmer picked 54 apples. If he sells 65 of the apples, how many will he sell?

CH AL L ENGE Solve. 23. Anna had 8 pies. She cut each pie into 12 slices. If she wants to share her pies equally with 20 people, how many whole slices can each person get?

Level E

| Chapter 9 - 2

If she does not want to waste any pie, how could she split the pie as fairly as possible?

| Lighthouse MATH

185

Read the problem. Then solve. Simplify if needed.

9 - 3 | Reciprocals Multiply. Write your answer in simplest form. 3

1. 10 × 6

DAILY REV IE W

2. 12 × 4

3. 9 × 8

4. 10 × 7

5. 15 × 4

L E A R N A ND C ONNEC T When we flip the numerator and denominator of a fraction, we create its reciprocal. When we multiply a fraction by its reciprocal, the answer is always 1.

Whole numbers can be written as a fraction over 1. Rewrite and flip to find the reciprocal of a whole number.

Fraction

Reciprocal

Multiply to check

4 9

9 4

4 × 9 = 36 = 1 9 4 36

Whole Number

Reciprocal

Multiply to check

1 4

4 × 1 = 4 =1 1 4 4

4= 4 1

AP P LY Switch the numerator and denominator to write the reciprocals. Then multiply to check. 4

1. 7

2. 3

3. 10

Check:

4 7 7 × 4 =

1 3 3 × 1 =

9 10 10 × 9 =

2 9 9 × 2 =

5. 12

6. 3

7. 7

8. 8

Check:

11 12 12 × 11 =

4 3 3 × 4 =

2 7 7 × 2 =

1 8 8 × 1 =

Vocabulary Reciprocal - an inverted fraction; found by switching the numerator and denominator

186

4. 9

Level E

| Chapter 9 - 3

| Lighthouse MATH

Exercise | 9 - 3 Name

Write the reciprocals. 3

1. 5

2. 11

3. 7 Remember: A whole number can be written as a fraction over 1. 4 4= 1

4. 9

5. 5

6. 15

7. 6

8. 5

9. 9

10. 7

11. 11

12. 5

13. 3

14. 5

15. 11

16. 7

17. 2

18. 13

19. 9

20. 12

21. 3

22. 17

23. 19

24. 9

25. 3

26. 5

27. 11

28. 7

29. 2

31. 9

32. 12

33. 3

34. 17

30. 13

Circle the pairs that are reciprocals. 1

36. 11 , 10

37. 3 , 16

38. 5 , 5

39. 2 , 5

40. 20, 4

41. 13 , 13

42. 7 , 4

44. 9 , 9

45. 11 , 11

46. 6, 6

43. 2 , 17

35. 4 , 4

CH AL L ENGE Solve. What do you notice about the answers? 47. 8 ÷ 2 = 1

8× 2 =

12 ÷ 4 = 1

12 × 4 = Level E

| Chapter 9 - 3

| Lighthouse MATH

187

9 - 4 | Dividing Fractions Write the reciprocal. DAILY REV IE W

1. 4

2. 5

3. 6

4. 8

L E A R N A ND C ONNEC T To divide by a fraction, multiply by the reciprocal instead.

Set up the problem.

3 ÷ 1 5 10

KEEP the first number the same.

CHANGE ÷ to ×.

FLIP the second number.

3 5

1 10

3 5

Multiply the numerators and denominators and simplify.

3 × 10 = 30 = 6 = 6 5 1 5 1

10 1

AP P LY Rewrite the problem with multiplication. Remember: keep, change, flip. 2

1. 3÷ 3

5. 5 ÷ 3

188

4. 9 ÷ 14

2. 8 ÷ 3

3. 6 ÷ 10

7. 5 ÷ 10

6. 6÷ 4

Level E

| Chapter 9 - 4

| Lighthouse MATH

4 1 7 ÷ 2

Exercise | 9 - 4 Name

1. 4 ÷ 3

2. 4 ÷ 2

3. 8 ÷2

6. 4 ÷3

7. 5 ÷ 2

8. 7 ÷6

11. 10 ÷ 2

12. 8 ÷ 10

17. 6 ÷ 6

18. 2 ÷ 5

16. 5÷ 5

4. 3÷ 5

5. 3 ÷ 4

6 1 10 ÷ 2

10. 4 ÷ 10

13. 5 ÷ 3

14. 3 ÷ 6

15. 4 ÷ 8

19. 10 ÷ 3

20. 5 ÷ 8

CH AL L ENGE Solve each problem. Simplify if necessary. 3 21. George can ride his bike 10 miles in one minute. His friend lives 43 miles away. How long will it take George to bike to his friend’s house? Hint: Divide the distance by his speed.

Level E

| Chapter 9 - 4

22. Miss Miller’s car has 87 of a tank of gas. 2 If she uses 10 of a tank each day, how many days will the gas last?

| Lighthouse MATH

189

Solve. Remember: keep, change, flip.

9 - 5 | Chapter Review Divide. Write your answer in simplest form. 1

1. 4 ÷ 3

DAILY REV IE W

2. 10 ÷ 3

3. 5 ÷ 3

4. 2 ÷ 3

L E T ' S REV I EW Multiplying Fractions

Cross Simplifying

Multiply the numerators. Multiply the denominators.

Divide the diagonals by the same number. Then, multiply. 2 × 5 15 6

2 × 4 = 8 3 5 15

1 × 1 = 1 3 3 9

2 and 6 can both be divided by 2. 5 and 15 can both be divided by 5.

Finding Reciprocals

Dividing Fractions

Flip the numerator and denominator.

Keep the first number, change ÷ to ×, and flip the second number to its reciprocal.

3 6

6 3

1 4

1 ÷ 3 3 4

1 × 4 = 4 3 3 9

AP P LY Multiply. Write your answer in simplest form. 1. 2 × 5

2. 4 × 10

3. 5 × 9

4. 5 × 8

6. 10 × 7

7. 6 × 9

8. 3 × 10

5. 10 × 3

190

Level E

| Chapter 9 - 5

| Lighthouse MATH

5. 2 ÷ 6

Exercise | 9 - 5 Name

Divide. Write your answer in simplest form. 1. 9 ÷ 7

2. 8 ÷ 6

3. 14 ÷ 5

4. 7 ÷ 5

5. 6 ÷ 8

6. 10 ÷ 4

7. 6 ÷ 18

8. 2 ÷ 7

9. 9 ÷ 2

10. 2 ÷ 4

11. 12 ÷ 7

12. 16 ÷ 2

13. 4 ÷ 6

14. 8 ÷ 5

15. 6 ÷ 5

17. 7 ÷ 3

18. 6 ÷ 3

19. 8 ÷ 5

20. 5 ÷ 4

25. 3 × 4

16. 20 ÷ 4

21. 4 × 9

22. 6 × 12

23. 8 × 21

24. 4 × 5

26. 6 ÷ 3

27. 4 ÷ 8

28. 4 ÷ 3

29. 5 ÷ 2

30. 2 ÷ 4

31. 9÷ 4

32. 8 × 5

33. 7 × 3

34. 2 × 6

35. 4 ÷ 7

37. 5 × 6

38. 8 ÷ 3

39. 3÷ 5

40. 3 × 8

36. 3 ÷ 3

Level E

| Chapter 9 - 5

| Lighthouse MATH

Solve. Write your answer in simplest form.

191

9 - 6 | Cumulative Review

Solve. 1.

3 − 2

8 × 1

2 × 1

4 + 5

9 × 3

1 × 1

6 − 2

4 × 4

1 × 3

10.

8 × 7

11.

6 + 8

12.

6 + 5

13.

3 + 7

14.

3 × 2

15.

7 + 5

16.

4 × 8

17.

3 + 6

18.

6 + 1

19.

5 + 2

20.

18 − 9

21.

5 + 4

22.

9 − 4

23.

9 × 2

24.

6 × 5

25.

8 + 8

26.

8 + 1

27.

15 − 5

28.

4 + 1

29.

8 × 3

30.

2 + 7

31.

12 − 7

32.

3 + 1

33.

9 × 6

34.

5 × 2

35.

2 × 8

36.

9 × 4

37. 8 48

38. 4 20

39. 7 56

40. 7 14

41. 2 12

42. 9 72

43. 6 30

44. 6 48

45. 9 81

46. 9 54

47. 5 35

48. 1 7

49. 2 16

50. 5 25

51. 3 15

52. 3 9

53. 2 4

54. 3 9

192

Level E

| Chapter 9 - 6

| Lighthouse MATH

Exercise | 9 - 6 Name

Add. 1.

788 + 971

528 + 650

914 + 774

3,595 + 2,238

3,779 + 5,071

478 − 403

823 − 427

7,172 − 1,677

10.

4,698 − 1,519

12.

104 × 4

13.

5,928 × 5

14.

2,537 × 2

15.

39 × 91

Subtract. 6.

508 − 12

Multiply. 11.

1,256 × 7

16. 5 474

17. 9 577

18. 2 695

19. 9 8,793

20. 96 5,703

Divide.

Subtract. Write your answer in simplest form. 21. 10 − 10

22. 7 − 4

23. 3 − 6

24. 12 − 3

25. 8 − 4

27. 15 − 3

28. 7 − 14

29. 4 − 6

30. 5 − 3

26. 6 − 3

Level E

| Chapter 9 - 6

| Lighthouse MATH

193

10 C H A P T E R

194

In Chapter 10, we will learn about

Decimals Fractions can also be written using place value. We call these numbers decimals because we put a decimal point between the wholes and parts. • We will write a fraction with a denominator of 10 as a number with one decimal place. • We will write a fraction with a denominator of 100 as a number with two decimal places. • We will write a fraction with a denominator of 1,000 as a number with three decimal places. • We will compare and order decimals. • We will round decimals. • We will change fractions to decimals. • We will change decimals to fractions.

195

10 - 1 | Tenths Rewrite each fraction to have 10 as the denominator. DAILY REV IE W

1 2 =

1 5 =

4 5 =

2 2 =

3 5 =

L E A R N A ND C ONNEC T Decimals are another way of writing fractions. When a fraction has a denominator of 10, the numerator tells us the number of tenths. Write the whole number, then write a decimal point. Write the numerator as the tenths.

4 1 10

Whole number

ones

tenths

Decimal point

1.4 We say one and four tenths. Decimal

AP P LY Write the amount shaded as a fraction and as a decimal. 1.

10 =

Vocabulary Fraction - a way to write a number that shows part of a whole Decimal - a way to write a number that shows part of a whole using place value and a decimal point Numerator - the top number in the fraction Denominator - the bottom number in a fraction that is the total number of equal parts in the whole

196

Level E

| Chapter 10 - 1

| Lighthouse MATH

10 =

Exercise | 10 - 1 Name

Write each fraction as a decimal. 2

2. 10

3. 10

7. 1 10

8. 3 10

9. 5 10

10. 10 10

14. 1 10

15. 10

16. 10 10

17. 6 10

13. 2 10

4. 10

5. 10

6. 10

11. 7 10

12. 4 10

18. 5 10

19. Six tenths

20. Four and nine tenths

21. Four tenths

22. Nine and five tenths

23. Fourteen and seven tenths

24. Two and one tenth

25. Five and four tenths

26. Six and three tenths

1. 10

Write the decimal in words. 27. 0.6

28. 1.2

Six

29. 8.1

One and

Eight and

CH AL L ENGE Read the problem. Then solve. 30. A group of friends hiked a trail. Before taking a break, they 3 5 hiked 10 of a mile. After the break, they hiked 10 of a mile. How far did they hike, written as a decimal?

Level E

| Chapter 10 - 1

| Lighthouse MATH

197

10 - 2 | Hundredths Write a decimal for each number. DAILY REV IE W

1 10 =

6 10 =

9 10 =

Four-tenths =

L E A R N A ND C ONNEC T A fraction with a denominator of 100 can be written as a number with two decimal places. The numerator tells us the number of hundredths. Write the whole number, then write a decimal point. Write the numerator as the hundredths. You may need to add a zero to make sure the number ends up in the hundredths place.

3 = 100

36 = 1 100

ones

0 ones

tenths hundredths

0.03 We say three hundredths.

tenths hundredths

1.36 We say one and thirty-six hundredths.

Tip!

r. That’s Count the zeros in the denominato d. nee you es how many decimal plac

AP P LY Write the amount shaded as a decimal. 1.

100

198

100

Level E

| Chapter 10 - 2

| Lighthouse MATH

Exercise | 10 - 2 Name

Write the fraction as a decimal. 5

1. 100

3. 100

2. 6100

6. 12100

7. 100

11. 100

12. 13100

17. 3100

16. 19100

4. 11100

5. 100

8. 1100

9. 100

10. 25100

13. 8100

14. 100

15. 7100

18. 6100

19. 100

20. 100

21. Twenty-six hundredths

22. Five and five hundredths

23. Eighty hundredths

24. Ten and eleven hundredths

25. Three and three hundredths

26. Forty-seven hundredths

27. 1.35

One and

28. 0.09

Nine

29. 5.64

Five and

Write the decimal in words.

CH AL L ENGE Write the total amount shaded as a decimal. 30.

Level E

| Chapter 10 - 2

| Lighthouse MATH

199

10 - 3 | Thousandths Write a decimal for each number. DAILY REV IE W

99 100 =

7 100 =

8100 =

25100 =

L E A R N A ND C ONNEC T A fraction with a denominator of 1,000 can be written as a number with three decimal places. The numerator tells us the number of thousandths. Write the whole number, then write a decimal point. Write the numerator as the thousandths. You may need to add one or two zeros to make sure the number ends up in the thousandths place.

8 = 1,000

475 3 1,000 =

ones

tenths hundredths thousandths

0 ones

tenths hundredths thousandths

0.008 We say eight thousandths.

3.475 We say three and four hundred seventy-five thousandths.

AP P LY Write the fraction as a decimal. 1. 1,000

2. 1,000

3. 1,000

8. 1,000

938

9. 5 1,000

7. 16 1,000

4. 10 1,000

5. 1,000

6. 1,000

999

11. 1,000

501

12. 1,000

10. 1,000

Vocabulary Thousandth - One part out of one thousand equal parts of a whole

200

Level E

| Chapter 10 - 3

| Lighthouse MATH

782

Exercise | 10 - 3 Name

Write a decimal for each number. 1. 1,000

2. 1,000

3. 1,000

6. 16 1,000

7. 1,000

938

8. 5 1,000

9. 1,000

11. 1,000

12. 1,000

13. 90 1,000

136

17. 1,000

18. 18 1,000

295

19. 1,000

16. 1,000

4. 10 1,000

5. 1,000

999

10. 1,000

14. 1,000

15. 17 1,000

348

20. 2 1,000

501

810

118

21. Ten and twenty-six thousandths

22. Five and five thousandths

23. Eighty thousandths

24. Ten and eleven thousandths

25. Thirty-three and thirty-five thousandths

26. Twenty and nine hundred thousandths

27. 0.108

One hundred eight

28. 80.003

Eighty and

29. 2.076

Two and

Write the decimal in words.

CH AL L ENGE Answer the question. Explain. 30. Marcus says that 20.900 is greater than 20.9 because 20.900 has more digits. Is Marcus correct?

Level E

| Chapter 10 - 3

| Lighthouse MATH

201

10 - 4 | Decimal Place Value Write the fraction as a decimal. DA ILY REV IE W

8 10 =

4 100 =

54 100 =

807 1,000 =

L E A R N A ND C ONNEC T We can use a place value chart to find the place or the value of digits in a decimal.

631.981 hundreds

tens

ones

tenths

hundredths

thousandths

The digit 6 is in the hundreds place. It has a value of 600. The digit 8 is in the hundredths place. It has a value of 0.08.

AP P LY

Read the number. Then answer the questions. 1.

679.341

492.063

Which digit is in the tens place?

Which digit is in the hundreds place?

What is the value of the tens digit?

What is the value of the hundreds digit?

Which digit is in the hundredths place?

Which digit is in the thousandths place?

What is the value of the hundredths digit?

What is the value of the thousandths digit?

Vocabulary Decimal Place Value - what a digit is worth based on its spot to the right of the decimal point

202

Level E

| Chapter 10 - 4

| Lighthouse MATH

Exercise | 10 - 4 Name

Write the value of the underlined digit. 1. 54.12

2. 0.87

3. 12.34

4. 199.01

5. 945.67

6. 8.1

7. 376.32

8. 21.50

9. 90.08

10. 403.45

11. 67.89

12. 0.22

13. 88.43

14. 31.76

15. 0.55

16. 442.10

17. 95.61

18. 19.84

19. 50.00

20. 6.73

21. 983.14

22. 27.99

23. 11.02

24. 660.36

25. One hundred and fifty-five hundredths

26. Fourteen and eighty-two hundredths

27. Two and three hundredths

28. Six hundredths

29. Nine hundred seven and one tenth

30. Eight and seven tenths

Write the decimal for each number.

CH AL L ENGE Solve the riddle. 31. I am a number with five digits. I have a one in the hundreds place and a nine in the hundredths place. The tenths place is five less than the hundredths place. There are no ones, and there are eight tens. What number am I?

Level E

| Chapter 10 - 4

| Lighthouse MATH

203

10 - 5 | Comparing Decimals Write the value of each underlined digit. DAILY REV IE W

153.12

6.27

122.34

9.81

L E A R N A ND C ONNEC T Which time is fastest?

Time 1

Time 2

3.482 min

3.487 min

Write > for greater than. Write < for less than.

Line up the decimal points.

Start by comparing the digits in the highest place value.

If needed, move to the right. Compare the digits.

3.482 3.487

3=3

4=4

8=8

2<7

Time 2 is fastest because 3.482 < 3.487.

We can write the numbers in order from least to greatest: 3.482; 3.487

AP P LY Shade in the models to represent the decimals. Write <, >, or = to compare. 1. 0.4

204

0.04

2. 0.8

Level E

0.6

| Chapter 10 - 5

3. 0.3

| Lighthouse MATH

0.30

Exercise | 10 - 5 Name

Write <, >, or = to compare the decimals. 1. 3.42 3. 4

2. 9.0

3.2

4. 4.21

0.4

Tip!

9.00

Zeros can be added to or dropped from the end of decimals.

0.42

0.2 = 0.20

5. 0.70

0.7

6. 6.432

6.5

7. 15.78

15.09

8. 12.1

1.21

9. 8.00

0.800

10. 12.02

12.020

11. 3.25

32.5

12. 1.08

1.80

13. 0.94

0.95

14. 1.75

1.7

15. 0.68

0.6

Write the numbers in order from least to greatest. ,

17. 1.32; 2.03; 1.322

18. 0.091; 0.4; 0.8

19. 0.199; 0.35; 0.06

20. 6.05; 6.1; 6.87

21. 4.55; 4.17; 4.040

22. 9.6; 9.89; 9.56

23. 0.584; 0.467; 0.1

24. 2.02; 2.761; 2.935

25. 0.583; 0.01; 0.744

16. 0.04; 0.4; 0.004

CH AL L ENGE 26. Which city had the most rainfall?

Monthly Average Rainfall

27. Which city had the least rainfall?

City

Rainfall (in.)

Springfield

2.450

Riverside

2.389

Oakdale

2.512

Maplewood

2.467

28. Write the decimals in order from least to greatest. ,

Level E

| Chapter 10 - 5

| Lighthouse MATH

205

10 - 6 | Rounding Decimals Compare the decimals using <, >, or =. DAILY REV IE W

0.6

0.60

3.45

3.54

1.208

1.28

7.5

7.500

L E A R N A ND C ONNEC T We can follow rules to round numbers to any place value. Round 845.3267 to the nearest whole number. Mark the place you are rounding.

Look to the right of that digit.

When we round to the nearest whole number, we round to the ones place.

845.3267

Use the rules for rounding.

Change the rest of the digits to 0.

4 or lower Marked digit stays the same

845.0000

5 or higher Marked digit goes up

845.3267

Tip! Zeros at the end of a decimal can be dropped.

Let's round 845.3267 to different places. Tenths

845.3267

Hundredths

845.3

845.3267

845.33

Thousandths

845.3267

845.327

AP P LY Round to the nearest whole number. 1. 3.28

2. 16.823

3. 27.51

4. 29.79

7. 32.82

8. 41.23

11. 21.257

12. 17.279

Round to the nearest tenth. 5. 4.78

6. 1.837

Round to the nearest hundredth. 9. 12.817

206

10. 7.193

Level E

| Chapter 10 - 6

| Lighthouse MATH

Exercise | 10 - 6 Name

Round to the nearest whole number. 1. 3.79

2. 121.518

3. 1.89

4. 78.4

5. 12.13

6. 42.18

7. 15.218

8. 127.191

9. 892.01

10. 21.45

11. 27.52

12. 32.009

Round to the nearest tenth. 13. 4.27

14. 53.998

15. 5.952

16. 23.189

17. 892.12

18. 289.23

19. 43.109

20. 389.143

21. 498.138

22. 32.791

23. 28.108

24. 389.821

Round to the nearest hundredth. 25. 8.208

26. 23.981

27. 4.892

28. 37.291

29. 12.340

30. 39.189

31. 37.891

32. 398.891

33. 5.298

34. 238.983

35. 15.962

36. 289.127

37. 17.8347

38. 9.0563

39. 1.7854

40. 0.9347

41. 25.8726

42. 1.2243

43. 30.9983

44. 1.2987

Round to the nearest thousandth.

CH AL L ENGE Circle the correct answer. 45. Which numbers have the same value when rounded to the nearest hundredth? A. 3.478 & 3.472 C. 5.753 & 5.763

B. 4.562 & 4.559 D. 3.128 & 3.118

Level E

| Chapter 10 - 6

46. Which number has the same value when rounded to the nearest tenth and when rounded to the nearest hundredth? A. 7.238 C. 9.421

| Lighthouse MATH

B. 8.702 D. 4.210

207

10 - 7 | Changing Fractions to Decimals Round each number to the nearest hundredth. DAILY REV IE W

36.837

2.982

0.117

41.288

L E A R N A ND C ONNEC T 7 20

We can write fractions as decimals.

35 100 100

Write 20 as a decimal.

0.35 0

Find an equivalent fraction with a denominator of 10, 100, or 1,000.

Write it as a decimal.

×5 35 = 0.35 100

7 = 35 20 100

×5

AP P LY Write the fraction as a decimal. 1. 20 =

2. 4 =

3. 5 =

4. 5 =

5. 10 =

6. 2 =

7. 4 =

8. 50 =

10. 20 =

11. 50 =

12. 50 =

9. 50 =

208

Level E

| Chapter 10 - 7

| Lighthouse MATH

Exercise | 10 - 7 Name

Write the fraction as a decimal. 1. 10 =

2. 10 =

3. 100 =

4. 2 =

5. 4 =

6. 4 =

7. 5 =

8. 5 =

9. 5 =

10. 20 =

12. 20 =

13. 25 =

14. 25 =

15. 25 =

16. 50 =

17. 50 =

18. 50 =

19. 20 =

20. 20 =

21. 20 =

22. 100 =

23. 100 =

24. 100 =

25. 20 =

27. 25 =

28. 20 =

29. 4 =

30. 25 =

32. 10 =

33. 5 =

34. 100 =

35. 20 =

26. 5 =

31. 50 =

11. 20 =

CH AL L ENGE Solve. 7 13 36. Max ran 10 of a mile on Monday and 20 of a mile on Tuesday. Write both distances as decimals. On which day did Max run farther?

Level E

| Chapter 10 - 7

| Lighthouse MATH

209

10 - 8 | Changing Decimals to Fractions Write each fraction as a decimal. DAILY REV IE W

4 5 =

3 20 =

16 50 =

2 5 =

L E A R N A ND C ONNEC T We can write decimals as fractions. Use decimal place value to write as a fraction over 10. Write 0.6 as a fraction.

ones

tenths

= 6 10

6 is in the tenths place.

Use decimal place value to write as a fraction over 100.

Write 4.32 as a fraction.

ones

tenths hundredths

32 100

There are 4 ones and 32 hundredths.

Simplify. 6 = 3 10 5

Simplify. 32 8 4 100 =4 25

AP P LY Write the decimal as a fraction. 1. 0.3 = 10

2. 0.4 = 10

3. 0.9 = 10

4. 0.7 = 10

5. 0.11 = 100

6. 0.99 = 100

7. 0.67 = 100

8. 0.17 = 100

9. 0.15 =

10. 0.6 =

11. 0.27 =

12. 0.81 =

210

Level E

| Chapter 10 - 8

| Lighthouse MATH

Exercise | 10 - 8 Name

1. 0.1 =

2. 0.3 =

3. 0.7 =

4. 0.5 =

5. 0.2 =

6. 0.50 =

7. 0.75 =

8. 0.10 =

9. 0.20 =

10. 0.40 =

11. 0.15 =

12. 0.47 =

13. 0.49 =

14. 0.4 =

15. 0.6 =

16. 0.8 =

17. 0.9 =

18. 0.25 =

19. 0.12 =

20. 0.02 =

21. 0.48 =

22. 0.32 =

23. 0.05 =

24. 0.31 =

25. 1.41 =

26. 4.92 =

27. 6.14 =

28. 2.55 =

29. 6.21 =

30. 8.58 =

31. 9.67 =

32. 2.87 =

33. 8.45 =

34. 6.79 =

35. 7.87 =

36. 8.19 =

Write the decimals as fractions. Simplify.

CH AL L ENGE Write the fractions as decimals. 32

37. 10 =

223

38. 10 =

Level E

39. 100 =

| Chapter 10 - 8

| Lighthouse MATH

132

40. 100 =

211

10 - 9 | Chapter Review Write each decimal as a simplified fraction. DAILY REV IE W

0.85

0.3

0.24

0.65

L E T ' S REV I EW Writing Fractions as Decimals Fractions with denominators of 10, 100, or 1,000 can be written as a decimal. Count the number of zeros to know how many decimal places to use. 168 3 1,000 = 3.168

ones

tenths hundredths thousandths

Three and one hundred sixty-eight thousandths

decimal

Rounding Decimals

Comparing Decimals

If the digit to the right is 5 or more, round up. If the digit to the right is 4 or less, round down.

Start comparing in the highest place value. Move right until the digits are different. Compare.

4193.168 rounded to the nearest tenth is 4193.2

93.2 > 93.168

AP P LY Write the amount shaded as a decimal. 1.

212

Level E

| Chapter 10 - 9

| Lighthouse MATH

Exercise | 10 - 9 Name

Write the fraction as a decimal. 3

1. 4 10 =

3. 100 =

4. 1,000 =

6. 8 1,000 =

7. 7610 =

8. 24 100 =

11. 5 =

2. 1,000 =

5. 25 10 = 3

9. 4 =

10. 25 =

12. 50 =

Write the value of the underlined digit. 13. 4.256

14. 18.19

15. 5.093

16. 26.032

17. 0.936

18. 10.305

21. 15.004

15.01

24. 25.618

22.845

Compare using <, >, or =. 19. 96.04

96.009

20. 4.03

22. 0.999

23. 38.900

8.95

38.9

25. 592.046

26. 403.945

27. 324.683

28. 142.142

31. 324.683

32. 142.142

Round to the nearest whole number.

Round to the nearest tenth. 29. 592.046

30. 403.945

Write the decimal as a fraction. 33. 0.4

34. 0.5

35. 0.15

36. 0.10

37. 4.96

38. 1.32

39. 9.29

40. 3.58

Level E

| Chapter 10 - 9

| Lighthouse MATH

213

10 - 10 | Cumulative Review

Solve. 1.

15 + 7

8 + 9

3 × 6

7 × 3

9 × 3

13 − 4

16 − 9

9 + 2

4 + 3

10.

10 − 6

11.

1 + 3

12.

8 − 1

13.

9 × 5

14.

9 − 8

15.

10 − 7

16.

8 × 8

17.

10 − 8

18.

7 × 1

19.

2 + 1

20.

16 − 7

21.

8 × 9

22.

14 + 2

23.

13 − 7

24.

6 − 1

25.

12 − 7

26.

2 + 4

27.

1 × 6

28.

3 × 7

29.

3 × 8

30.

5 × 1

31.

12 − 4

32.

8 + 3

33.

7 − 4

34.

12 − 6

35.

5 − 4

36.

3 × 3

37. 5 30

38. 2 18

39. 6 12

40. 8 24

41. 7 28

42. 9 9

43. 9 27

44. 6 18

45. 6 48

46. 3 15

47. 1 8

48. 9 18

49. 1 2

50. 9 72

51. 8 72

52. 2 8

53. 3 21

54. 2 10

214

Level E

| Chapter 10 - 10

| Lighthouse MATH

Exercise | 10 - 10 Name

Add. 1.

827 + 293

984 + 242

231 + 828

1,872 + 7,271

7,166 + 4,092

717 − 516

802 − 139

5,900 − 2,564

10.

6,984 − 4,425

12.

217 × 7

13.

5,400 × 3

14.

6,200 × 3

15.

37 × 18

Subtract. 6.

435 − 376

Multiply. 11.

110 × 6

Divide. 17. 6 348

18. 5 1,099

19. 6 3,763

20. 33 3,282

16. 7 158

Multiply the fractions. Write the answer in simplest form. 21. 2 × 4

22. 3 × 6

23. 5 × 2

24. 8 × 3

25. 9 × 10

27. 5 × 9

28. 12 × 14

29. 15 × 22

30. 16 × 21

26. 7 × 15

Level E

| Chapter 10 - 10

| Lighthouse MATH

215

11 C H A P T E R

216

In Chapter 11, we will learn about

Addition and Subtraction of Decimals We can add and subtract decimals using place value. When adding and subtracting decimals, it is important to keep your work neat and organized. • We will add decimals. • We will subtract decimals. • We will add and subtract money amounts. • We will estimate sums and differences of decimals. • We will solve word problems.

217

11 - 1 | Adding Decimals Write each number as a decimal. 2. Six tenths

1. Three and two tenths

DAILY REV IE W

3. One and four tenths

4. Ten and two hundredths

L E A R N A ND C ONNEC T A bag of pretzels weighs 1.2 ounces and a cup of juice weighs 3.95 ounces. How much do they weigh altogether? To find the total, add

Line up the decimal points.

and

Put zeros in the empty spaces.

1.2 + 3.95

1.20 + 3.95

Start adding from the right. Regroup if needed. Move left to the next place value and repeat. 1.20 + 3.95 5

1.20 + 3.95 15

1.20 + 3.95 5.15

The total weight is 5.15 ounces.

AP P LY Add. Put zeros in the empty spaces. 1.

2. +

0 . 4 0 . 5 .

1 . 2 5 + 2 . 7 . 6.

2 . 4 + 6 . 5 1

218

7. +

Level E

5 . 3 2 . 6

| Chapter 11 - 1

2 9 . 7 + 4 . 6 .

4 . 5 1 + 3 . 2 8 . 8. 1 2 . 1 + 3 . 2

| Lighthouse MATH

7 . 7 + 2 9 . 9

Exercise | 11 - 1 Name

Add. 1.

4.6 + 27.9

5.75 + 4.25

18.94 + 7.37

56.8 + 34.5

9.8 + 4.38

27.5 + 18.9

6.77 + 5.44

4.6 + 37.8

8.91 + 7.09

10.

13.65 + 9.5

11.

68.4 + 2.7

12.

5.99 + 4.99

13.

23.42 + 7.18

14.

7.9 + 8.49

15.

6.72 + 4.84

16.

78.35 + 2.87

17.

29.04 + 82.30

18.

3.91 + 5.04

19. 7.85 + 6.47

20. 38.4 + 25.9

21. 9.93 + 32.18

22. 56.7 + 14.6

23. 4.82 + 18.29

24. 19.5 + 12.65

25. 83.8 + 17.5

26. 36.44 + 3.5

Read the problem. Then solve. 27. Helen buys 6.85 pounds of red lentils and 4.49 pounds of black lentils. What is the total weight of the lentils she buys?

28. A family walked 15.8 miles one day and 12.5 miles the next day. How many miles did they walk in all?

CH AL L ENGE Solve. 29. Three boards are put end to end. They are 14.6 feet, 9.85 feet, and 12.7 feet long. What is the total length?

Level E

| Chapter 11 - 1

| Lighthouse MATH

219

Rewrite and solve.

11 - 2 | Subtracting Decimals Add. 1.

DAILY REV IE W

45.8 + 16.3

29.7 + 53.6

18.5 + 44.9

67.4 + 22.8

36.6 + 36.6

L E A R N A ND C ONNEC T A rope is 25.5 feet long. Tim cuts off 18.75 feet. How long is the rope now? To find the amount left, subtract

Line up the decimal points. 25.5 − 18.75

from

Put zeros in the empty spaces. 25.50 − 18.75

Start subtracting from the right. Regroup if needed. Move left to the next place value and repeat. 4 10

14 4 4 10

14 14 1 4 4 10

25.50 − 18.75 5

25.50 − 18.75 .75

25.50 − 18.75 6.75

25.50 − 18.75 06.75

The rope is 6.75 feet long now.

AP P LY Subtract. Trace the zeros in the empty spaces. 1.

2. −

2 9 . 5 1 4 . 8 .

2 4 . 8 0 − 1 1 . 7 5 . 6.

−

220

3 4 . 0 1 2 . 6

7. 1 8 . 9 5 − 7 . 3 8

Level E

| Chapter 11 - 2

4 0 . 5 0 − 1 8 . 2 5 .

1 5 . 8 2 − 6 . 3 5 . 8. 2 5 . 6 2 − 1 4 . 7 1

| Lighthouse MATH

1 0 . 0 0 − 4 . 2 5

Exercise | 11 - 2 Name

Subtract. 1.

15.42 − 8.67

30.05 − 12.48

9.10 − 4.82

50.00 − 23.15

12.8 − 7.94

100.2 − 45.7

6.03 − 2.55

24.16 − 5.90

8.40 − 3.27

10.

71.5 − 8.6

11.

40.10 − 18.25

12.

5.20 − 0.88

13.

13.62 − 9.70

14.

80.00 − 44.44

15.

19.35 − 1.46

16.

2.10 − 0.95

17.

65.40 − 37.81

18.

10.05 − 4.16

19. 43.25 − 24.5

20. 7.4 − 6.25

21. 90.2 − 33.73

22. 15.02 − 8.13

23. 0.6 − 0.47

24. 200 − 125.50

25. 11.11 − 5.55

26. 8.3 − 7.91

Read the problem. Then solve. 27. A tank holds 60.5 gallons. It has 18.75 gallons now. How many more gallons will fill the tank?

28. A tree was 4.62 feet tall last year. Now it is 5.1 feet tall. How much did it grow?

CH AL L ENGE Solve. 29. 15 − 0.85 − 9.4 =

Level E

| Chapter 11 - 2

| Lighthouse MATH

221

Rewrite and solve.

11 - 3 | Adding and Subtracting Money Subtract. 1.

DAILY REV IE W

45.8 − 7.65

64.78 − 8.2

55.46 − 7.08

51.70 − 12.49

L E A R N A ND C ONNEC T Eddie has a 5-dollar bill. He wants to buy a ball for $3.68. How much money will he get back? The money Eddie gets back is called change. To find how much change Eddie will get, subtract $ from $ . To add or subtract money, line up the decimals and add or subtract from right to left. Line up the decimals. Put zeros in the empty spaces.

Start subtracting from the right. Regroup if needed. Move left to the next place value and repeat.

$5.00 − $3.68

9 4 10 10

9 4 10

9 4 10 10

$5.00 − $3.68 2

$5.00 − $3.68 32

$5.00 − $3.68 1 32

Bring the decimal down and write the dollar sign. 9 4 10 10

$5.00 − $3.68 $1.32

Eddie will get $1.32 in change.

AP P LY Solve. 1.

2. $ 8 . 0 0 − $ 1 . 0 5 $ .

$ 7 . 5 0 + $ 3 . 2 5 $ 6.

$ 2 . 7 8 + $ 5 . 8 3

222

4. $ 2 3 . 8 5 − $ 1 8 . 6 5 $

7. $ 5 . 8 6 − $ 3 . 0 9

Level E

| Chapter 11 - 3

$ 6 5 . 0 5 − $ 1 8 . 6 5 $ 8.

$ 1 4 . 0 6 − $ 6 . 7 0

| Lighthouse MATH

$ 1 0 0 . 8 3 + $ 1 2 . 6 7

Exercise | 11 - 3 Name

Solve. 1.

$24.90 + $5.75

$30.00 − $1.43

$16.20 + $9.05

$8.40 − $3.06

$72.52 + $2.15

$25.13 + $19.61

$77.80 − $6.02

$2.83 + $19.94

$85. − $19.63

10.

$243.10 + $3.07

11.

$12.03 + $16.48

12.

$98.92 − $84.80

13.

$14.63 + $12.90

14.

$35.21 − $16.07

15.

$4.81 + $10.53

Rewrite and solve. 16. $3.54 + $6.92

17. $8 + $5.84

18. $7.75 + $15.43

19. $99.03 − $22.40

20. $304.70 − $28.45

21. $430.33 − $8.99

22. $70.37 + $11.48

23. $40 − $22.80

24. Max has $5.45 and earns $12.85 for mowing the lawn. How much money does Max have now?

Read the problem. Then solve. 25. Helen starts with $25. She spends $18.68 on picnic supplies. How much money does Helen have left?

CH AL L ENGE Solve. 26. Leo starts with $20. He spends $5.47, $8.13, and $2.00 at three stores. How much money does he have left?

Level E

| Chapter 11 - 3

| Lighthouse MATH

223

11 - 4 | Estimating Sums and Differences Solve. 1.

DAILY REV IE W

$3.07 + $7.02

$5.62 − $2.14

$2.45 + $6.32

$7.14 + $9.49

L E A R N A ND C ONNEC T Mannie bought a notebook for $8.40 and a set of pens for $4.68. About how much money did he spend? We don’t need to find the exact amount. To estimate the total cost, round and the nearest whole number and then add. Round the first number. $8.40 + $4.68

Round the second number.

$8.00

$8.40 + $4.68

Add.

$8.00 $5.00

$8.40 + $4.68

$8.00 + $5.00 $13.00

Mannie spent about $13.00.

AP P LY Round to the nearest whole number. Then estimate the sum or difference. 1.

25.67 + 12.05

26 + 12

8.37 + 0.92

8 + 1

10.12 + 0.75

10 + 1

$17.32 − $8.53

$17 − $9

$3.65 − $0.80

$4 − $1

$9.72 − $3.10

$10 − $3

| Chapter 11 - 4

| Lighthouse MATH

Vocabulary Estimate - a close, but not exact answer

224

Level E

Exercise | 11 - 4 Name

14.25 + 3.4

25.45 − 13.83

20.50 − 9.75

10.

12.78 − 6.43

13.

7.30 + 9.85

−

16.75 − 8.5

18.30 − 4.60

14.60 + 3.19

11.

10.13 + 8.52

14.

6.57 + 7.35

−

8.90 + 1.35

23.40 + 5.06

6.75 + 2.50

12.

9.50 − 3.25

−

15.

15.10 − 7.85

−

Read the problem. Then solve. 16. Ann walked 4.87 miles, and Ruth walked 2.39 miles. About how much farther did Ann walk?

17. A puzzle costs $7.49, and a ball costs $3.27. About how much would you pay for both?

CH AL L ENGE Solve by estimating. 18. Justin bought a sandwich for $6.85 and a drink for $2.95. He paid with a $20 bill. About how much change should he receive?

Level E

| Chapter 11 - 4

| Lighthouse MATH

225

Round to the nearest whole number. Then estimate the sum or difference.

11 - 5 | Addition and Subtraction Word Problems Round to the nearest whole number, then estimate the answer. 1.

DAILY REV IE W

30.02 − 14.95

4.7 + 2.35

22.4 − 6.85

L E A R N A ND C ONNEC T Steven travels on a train for 26.73 miles and in a car for 4.54 miles. How many miles did Steven travel altogether? We need to add the miles from each part of his trip. How many miles did he travel by train? How many miles did he travel by car? 11

26.73 + 4.54 31.27

Steven traveled

miles in all.

Remember: When adding or subtracting ts. decimals, line up the decimal poin

AP P LY Solve. 1. A tomato plant started off 4.86 inches tall. After one week, it was 8.25 inches tall. How much did the plant grow?

2. A ribbon is 3.8 yards long. Abby used 2.64 yards of it. How much is left?

3. Sam had $6.78. He spent $4.24. How much money does he have left?

4. One tank has 2.4 gallons of water in it. Another tank has 4.23 gallons. How much water do they have altogether?

226

Level E

| Chapter 11 - 5

| Lighthouse MATH

Exercise | 11 - 5 Name

1. Judy bought 12.35 ounces of paprika and 8.75 ounces of black pepper. How many ounces of spices did she buy altogether?

2. A bottle holds 2.5 quarts of juice. Ken pours out 1.35 quarts. How many quarts of juice are left?

3. A store had 42.5 pounds of apples. They sold 18.75 pounds. How many pounds are left?

4. Harry bought paint for $8.45 and paper for $6.35. What was the total cost?

5. Paul had $20.00 and spent $13.45. How much money does he have left?

6. A tree grew 2.5 feet one year and 4.75 feet the next year. How much did the tree grow in all?

7. George saved $12.50 in March and $9.75 in April. How much did he save in total?

8. A bucket holds 12.6 pints of water. Ari uses 4.75 pints of it. How many pints are left?

9. Moses had 24.5 pounds of strawberries. He used 12.96 pounds to make pies. How many pounds are left?

10. John cuts 2.65 feet off of a wooden beam that is 14.9 feet long. How long is the beam now?

CH AL L ENGE Solve. 11. Rose had $50.00. She bought a shirt for $19.95 and a hat for $13.75. How much money does she have left?

Level E

| Chapter 11 - 5

| Lighthouse MATH

227

Solve.

11 - 6 | Chapter Review Solve. 1.

DAILY REV IE W

4.35 + 2.18

7.5 − 2.27

5.64 + 1.29

4.56 + 9.8

6.48 − 3.75

L E T ' S REV I EW Adding and Subtracting Decimals

Estimating Sums and Differences

Line up the decimals. Put zeros in any empty spaces. Add or subtract, regrouping as needed. Bring down the decimal.

Round each number. Add or subtract the rounded values.

12 7 2 10

8.3 + 4.92 13.22

8.30 − 4.92 3.38

$14.86 − $8.32

$15 − $8 $7

AP P LY Add. 1.

4.35 + 2.18

7.2 + 3.47

5.64 + 1.3

9.8 + 4.56

6.75 + 3.4

7.2 − 3.47

5.64 − 1.3

9.8 − 4.56

10.

6.75 − 3.4

Subtract. 6.

228

4.5 − 2.38

Level E

| Chapter 11 - 6

| Lighthouse MATH

Exercise | 11 - 6 Name

Solve. 1.

5.6 − 2.34

7.8 − 4.25

6.45 + 2.3

9.2 − 5.67

4.75 + 3.4

3.9 + 2.75

6.8 − 2.46

5.25 + 1.6

7.4 − 3.18

10.

9.35 + 2.4

11.

$11.20 − $6.30

12.

$4.75 + $3.90

13.

$10.00 − $2.48

14.

$6.85 + $2.75

15.

$9.40 − $3.27

Estimate the sum or difference by rounding to the nearest whole number. 16.

12.47 − 6.81

−

17.

9.63 + 4.52

18.

15.28 − 9.76

−

19. Leo bought a toy for $4.75 and a sticker for $1.25. How much money did he spend in all?

20. Amy has $10.00. She buys a book for $6.45. How much money does she have left?

21. A rope is 5.6 meters long. Sam cuts off 2.4 meters. How long is the rope now?

22. A jug has 3.75 liters of water. Emma pours in 1.25 more liters. How much water is in the jug now?

23. Noah buys two snacks. One costs $2.35, and the other one costs $1.86. How much money does he spend in all?

24. A cord is 8.5 feet long. A piece that is 3.2 feet long is cut off. How long is the cord now?

Level E

| Chapter 11 - 6

| Lighthouse MATH

229

Read the problem. Then solve.

11 - 7 | Cumulative Review

Solve. 1.

3 × 3

11 − 7

14 − 5

4 + 2

8 × 8

9 − 5

16 − 7

16 − 8

7 − 2

10.

1 × 2

11.

9 − 8

12.

15 − 9

13.

3 − 1

14.

3 + 5

15.

10 − 6

16.

8 × 6

17.

9 × 3

18.

3 + 6

19.

4 × 5

20.

8 + 1

21.

6 × 8

22.

2 × 8

23.

5 × 1

24.

7 − 3

25.

11 − 2

26.

8 + 3

27.

9 × 2

28.

13 − 4

29.

9 + 6

30.

15 − 7

31.

2 + 3

32.

9 + 1

33.

1 × 4

34.

4 + 3

35.

1 + 3

36.

7 + 9

37. 6 42

38. 4 12

39. 5 5

40. 9 36

41. 9 45

42. 9 72

43. 1 2

44. 7 35

45. 8 72

46. 4 20

47. 6 48

48. 8 16

49. 6 36

50. 4 24

51. 9 9

52. 8 8

53. 2 4

54. 3 15

230

Level E

| Chapter 11 - 7

| Lighthouse MATH

Exercise | 11 - 7 Name

Add. 1.

844 + 758

385 + 303

958 + 921

6,923 + 6,936

5,866 + 7,452

623 − 523

566 − 32

8,183 − 7,370

10.

9,672 − 4,118

12.

349 × 2

13.

1,084 × 3

14.

9,999 × 7

15.

75 × 16

Subtract. 6.

971 − 123

Multiply. 11.

287 × 8

16. 7 643

17. 4 184

18. 8 7,464

19. 6 4,728

20. 17 1,560

Divide.

Divide. Write your answer in the simplest form. 21. 2 ÷ 4

22. 5 ÷ 4

23. 9 ÷ 11

24. 14 ÷ 7

25. 15 ÷ 5

27. 3 ÷ 15

28. 21 ÷ 14

29. 10 ÷ 25

30. 27 ÷ 18

26. 18 ÷ 9

Level E

| Chapter 11 - 7

| Lighthouse MATH

231

12 C H A P T E R

232

In Chapter 12, we will learn about

Multiplying Decimals We use place value to multiply decimals. We can follow simple rules to find the product. • We will learn a trick to multiply a decimal by 10, 100, or 1,000. • We will multiply a decimal by a whole number. • We will multiply a decimal by a decimal. • We will multiply with zeros in the product. • We will multiply money amounts. • We will estimate products. • We will solve real-world problems.

233

12 - 1 | Multiplying a Decimal by 10, 100, or 1,000 Solve. 2. 5 × 100

1. 9 × 10

DAILY REV IE W

3. 8 × 1,000

4. 11 × 10

5. 7 × 100

L E A R N A ND C ONNEC T

To multiply a decimal by 10, 100, or 1,000, move the decimal point to the right. Add zeros to any empty places. 43.24 × 10

43.24 × 100

43.24 × 1,000

There is 1 zero in 10 so we move the decimal point 1 place to the right.

There are 2 zeros in 100 so we move the decimal point 2 places to the right.

There are 3 zeros in 1,000 so we move the decimal point 3 places to the right.

43.24

43.240

432.4

4,324

43,240

AP P LY Multiply. 1. 0.84 × 10

2. 0.31 × 100

3. 0.05 × 10

4. 1.26 × 100

5. 0.47 × 1,000

6. 6.9 × 10

7. 0.002 × 100

8. 15.75 × 10

234

Level E

| Chapter 12 - 1

| Lighthouse MATH

Exercise | 12 - 1 Name

Multiply. 1. 0.58 × 10

2. 0.19 × 100

3. 0.007 × 1,000

4. 4.26 × 10

5. 0.03 × 100

6. 1.5 × 1,000

7. 0.125 × 100

8. 0.9 × 10

9. 0.041 × 100

10. 2.88 × 100

11. 100 × 2.88

12. 100 × 0.6

13. 10 × 0.009

14. 1,000 × 12.4

15. 100 × 0.77

16. 1,000 × 0.025

17. 10 × 0.06

18. 100 × 67.3

19. 10 × 40

20. 1,000 × 0.00007

Fill in the missing factor. Choose from 10, 100, or 1,000. 21. 0.42 ×

= 4.2

22. 0.06 ×

23. 1.35 ×

= 13.5

24. 0.008 ×

25. 0.92 ×

= 92

26. 0.7 ×

= 70

27. 15.2 ×

= 152

28. 0.04 ×

= 40

29. 0.111 ×

30. 8.6 ×

= 8,600

31. 5.8 ×

= 580

= 60

Read the problem. Then solve. 33. A single building block is 0.85 centimeters tall. How tall will a tower of 100 of these blocks be?

34. One battery weighs 1.2 ounces. A crate has 1,000 batteries. What is the total weight of the batteries in the box?

CH AL L ENGE Multiply. 35. 0.47 × 10,000 =

36. 0.47 × 100,000 =

Level E

| Chapter 12 - 1

| Lighthouse MATH

37. 0.47 × 1,000,000 =

235

32. 6×

= 11.1

12 - 2 | Multiplying a Decimal by a Whole Number Solve. 1. 0.12 × 10

DAILY REV IE W

2. 0.05 × 100

3. 0.4 × 10

4. 1.1 × 100

5. 0.008 × 1,000

L E A R N A ND C ONNEC T When multiplying decimals, ignore the decimal point until the end.

Multiply like whole numbers.

Count the total decimal places in the problem.

5 3

0.85 × 7 595

Move from the right to place the decimal point.

The number of decimal places in the answer is the same as the total number of decimal places in the problem.

2 decimal places + 0 decimal places 2 decimal places

5.95

AP P LY

Multiply. Place the decimal point. 1.

2. 0 . 6 4 × 3 .

0 . 1 5 × 9 .

7. 1 . 2 5 × 8

236

4. 0 . 4 2 × 5 .

8. 3 . 7 × 2

Level E

5. 0 . 7 6 × 4 .

9. 0 . 9 1 × 7

| Chapter 12 - 2

0 . 8 × 6 .

10. 0 . 5 5 × 6

| Lighthouse MATH

7 . 8 × 9

Exercise | 12 - 2 Name

Multiply. 1.

1.5 × 3

2.78 × 5

8.04 × 2

3.6 × 4

6.52 × 6

39.9 × 7

5.12 × 8

10.25 × 4

6.3 × 3

10.

9.41 × 9

11.

12.06 × 5

12.

8.4 × 8

13.

1.55 × 6

14.

5.3 × 2

15.

4.88 × 7

16.

14.62 × 4

17.

21.05 × 8

18.

35.75 × 6

19. 1.4 × 4

20. 24.38 × 2

21. 11.09 × 7

22. 2.15 × 3

23. 1.7 × 6

24. 5.44 × 5

25. 13.62 × 8

26. 0.25 × 9

27. 31.14 × 4

28. 12.89 × 3

Read the problem. Then solve. 29. Lea buys 4 bags of flour. Each bag weighs 2.35 pounds. What is the total weight of the flour?

30. Sam drives 0.75 miles each day. How far does he travel over 8 days?

CH AL L ENGE Solve. 31. (4.25 × 6) + (0.88 × 9) =

Level E

| Chapter 12 - 2

| Lighthouse MATH

237

Rewrite and solve.

12 - 3 | Multiplying Decimals Solve. 1.

DAILY REV IE W

1.2 × 6

2.8 × 5

6.2 × 4

2.7 × 7

L E A R N A ND C ONNEC T A truck uses 0.13 gallons of gas per mile. If the truck travels 32.4 miles, how many gallons of gas does it use?

To find the gallons of gas used, multiply by . Set up the problem. The number with more non-zero digits goes on top.

Multiply. Ignore the decimal points.

32.4 × 0.13

32.4 × 0.13 972 + 3240 4212

Place the decimal point. The total number of decimal places in the answer is the same as the total number of decimal places in the problem. 1 decimal place + 2 decimal places 3 decimal places

4.212

The truck uses 4.212 gallons of gas.

AP P LY Multiply. Place the decimal point. 1.

3.9 × 0.3 .

0.72 × 0.8 .

3.99 × 4.55

45.2 × 1.2 +

238

Level E

| Chapter 12 - 3

| Lighthouse MATH

Exercise | 12 - 3 Name

Multiply. 1.

2.3 × 1.7

2.1 × 6.3

27.4 × 9.6

48.3 × 5.2

3.65 × 3.9

0.36 × 8.1

0.46 × 2.6

1.4 × 0.5

1.1 × 0.6

10.

59.2 × 0.45

11.

15.89 × 6.8

12.

4.96 × 1.5

13.

6.5 × 9.2

14.

62.86 × 2.4

15.

804.5 × 3.2

Rewrite and solve. 16. 1.31 × 8.4

17. 29.75 × 7.3

18. 68.6 × 0.13

19. 1.17 × 1.2

Read the problem. Then solve. 21. A rope is 2.3 yards long. How long are 2.5 ropes? © Lighthouse Curriculum. Copying strictly prohibited.

20. A recipe uses 3.25 tablespoons of sugar. How much sugar will be in 1.5 batches?

CH AL L ENGE Solve. 22. A baker made 2.5 batches of a cookie recipe that used 43 cups of sugar and 3.5 batches of a bread recipe that used 41 cups of sugar. Which used more sugar, the cookies or the bread?

Level E

| Chapter 12 - 3

| Lighthouse MATH

239

12 - 4 | Zeros in the Product Solve. 1.

DAILY REV IE W

5.6 × 4.2

9.9 × 4.9

3.14 × 6.8

L E A R N A ND C ONNEC T A paper clip is 2.4 cm wide. A piece of wire is 0.001 times the width of the paper clip. How wide is the wire? To find the width of the wire, multiply

Set up the problem. The number with more non-zero digits goes on top.

Multiply. Ignore the decimal points.

2.4 × 0.001

2.4 × 0.001 24

. Place the decimal point. Put zeros in empty places.

1 decimal place + 3 decimal places 4 decimal places

0.0024

The wire is 0.0024 cm wide.

AP P LY Multiply. Place the decimal point. 1.

2. 3.1 × 0.9

240

. 7. 0.28 × 0.02

Level E

0.64 × 0.09

6. 3.6 × 0.009

8.3 × 0.008

0.35 × 0.03

| Chapter 12 - 4

. 8.

1.7 × 0.005

| Lighthouse MATH

0.03 × 0.07

Exercise | 12 - 4 Name

Solve. 1.

0.6 × 0.6

0.7 × 0.2

0.01 × 0.9

0.05 × 0.3

0.73 × 0.9

0.53 × 0.08

0.27 × 0.09

0.86 × 0.05

9.2 × 0.007

10.

0.016 × 3.8

11.

1.86 × 0.0008

12.

89 × 0.00003

13.

0.45 × 0.005

14.

4.93 × 0.013

15.

2.773 × 0.02

Rewrite and solve. 16. 0.73 × 0.006

17. 0.15 × 1.8

18. 8.1 × 0.049

19. 3.2 × 0.009

Read each problem and then solve. 21. A piece of pipe is 0.32 inches long. A plumber needs a piece that is 0.002 times as long. How many inches is the new piece?

20. One zoo path is 0.25 miles long. Another path is 0.05 times as long. How long is the second path?

CH AL L ENGE 22. How do you know that 0.002 x 0.03 and 0.003 x 0.02 will be the same, even before you solve?

Level E

| Chapter 12 - 4

| Lighthouse MATH

241

12 - 5 | Multiplying Money Solve. 1.

DAILY REV IE W

1.25 × 6

16.35 × 0.2

2.7 × 0.5

L E A R N A ND C ONNEC T A train ticket costs $12.75. How much will it cost a group of 15 people to take the train? To figure out the total cost, multiply

Set up the problem. The number with more non-zero digits goes on top.

Multiply. Ignore the decimal point.

$12.75 × 15

$12.75 × 15 6375 12750 19125

Place the decimal point and dollar sign in your answer. 2 decimal places + 0 decimal places 2 decimal places

$191.25

The total cost is $191.25.

AP P LY Solve. 1.

$6.25 × 8 $ .

$3.27 × 6 $ .

$9.32 × 6 $ .

+ $ 5.

$2.54 × 3

$9.26 × 7

$3.41 × 5

242

Level E

| Chapter 12 - 5

| Lighthouse MATH

$2.48 × 77

. $7.13 × 16

Exercise | 12 - 5 Name

Solve. 1.

$6.61 × 5

$2.87 × 97

$5.78 × 70

$4.52 × 24

$7.41 × 7

$5.44 × 40

$6.22 × 90

$8.92 × 69

$7.02 × 2

10.

$8.06 × 52

11.

$9.92 × 10

12.

$8.67 × 4

13.

$4.46 × 57

14.

$2.99 × 20

15.

$4.08 × 45

Rewrite and solve. 17. $6.57 × 39

18. $2.02 × 75

19. $1.26 × 51

16. $3.46 × 12

Read each problem. Then solve. 20. George buys 8 candy bars. Each candy bar costs $2.55. How much money did he spend in all?

21. Oranges cost $2.49 per pound. How much will 3 pounds cost?

CH AL L ENGE 22. A cook charges $35.25 per hour. One job took 6.25 hours. How much will he charge?

Level E

| Chapter 12 - 5

| Lighthouse MATH

243

12 - 6 | Estimating Products Solve. DAILY REV IE W

2. 90 × 60 =

1. 30 × 400 =

3. 300 × 200 =

L E A R N A ND C ONNEC T Apples cost $5.90 per pound. Leah buys 8.7 pounds of apples. About how much does she pay? We don’t need to find the exact amount. To estimate the total cost, round and to the nearest whole number and multiply. Round the first number. 5.90 × 8.7

Round the second number.

5.90 × 8.7

Multiply.

6 × 9

5.90 × 8.7

6 9 54

She pays about $54 for the apples.

AP P LY Round to the nearest whole number, then multiply. 1.

3.24 × 5.6

58.7 × 2.4

4.66 × 8.2

244

9.33 × 0.86

4.81 × 13.5

59.8 × 0.53

Level E

| Chapter 12 - 6

2.99 × 4.67

5.65 × 6.1

25.8 × 7.6

| Lighthouse MATH

Exercise | 12 - 6 Name

Round to the nearest whole number, then multiply. 1.

8.03 × 0.68

5.21 × 6.4

7.8 × 5.1

10.

6.1 × 3.8

7.9 × 9.5

589.7 × 1.1

11.99 × 4.2

11.

8.9 × 6.6

69.8 × 4.5

32.18 × 17

6.6 × 5.8

12.

3.8 × 2.1

13. A bag of apples weighs 3.98 pounds. If there are 6 bags, about how many pounds of apples are there?

14. A length of ribbon is 11.36 inches long. Kelly has 12 ribbons. About how many inches of ribbon does Kelly have?

CH AL L ENGE Use the problem below to answer the question. 15.

16.23 × 4.71

Which would give a better estimate: Rounding to the nearest whole number or rounding to the nearest tenth? Explain.

Level E

| Chapter 12 - 6

| Lighthouse MATH

245

Read the problem. Estimate to find the answer.

12 - 7 | Multiplication Word Problems Solve. DAILY REV IE W

2. 31 × 6 =

1. 57 × 7 =

3. 79 × 3 =

L E A R N A ND C ONNEC T Tickets for the state fair cost $14.50. If 84 people buy tickets, what will be the total cost? We need to multiply the cost of a ticket by the number of tickets. How much does each ticket cost? How many tickets were bought? $14.50 × 84 5800 116000 121800 The total cost for 84 tickets is $1,218.00.

AP P LY Read the problem. Then solve. 1. Potatoes are $1.29 per pound. How much will 8 pounds cost?

2. Gas is $3.28 per gallon. How much will it cost to buy 11 gallons of gas?

3. If one folding chair weighs 4.8 pounds, how much will a stack of 8 chairs weigh?

4. The school is 4.8 miles from Kelly’s house. The zoo is 12 times as far. How far is the zoo?

246

Level E

| Chapter 12 - 7

| Lighthouse MATH

4. 11 × 9 =

Exercise | 12 - 7 Name

1. Bananas cost $0.72 per pound. How much will 15 pounds cost?

2. Oats cost $0.75 per pound. How much will 3.2 pounds cost?

3. A grocery store has 25 cases of soup. Each case weighs 18.8 pounds. How much do they weigh altogether?

4. One pound of flour has 3.6 cups. How many cups of flour are in a 5-pound bag?

5. A wooden board is 8.2 feet long. If a deck is built with 62 boards, what is the length of the deck?

6. At a zoo, penguins eat an average of 1.2 pounds of food per day. How many pounds of food are needed to feed 4 penguins for a day?

7. One shirt costs $12.52. How much will 8 shirts cost?

8. A jacket costs $25.99. How much will it cost to buy 3 jackets?

9. A train is traveling 52 miles per hour. How many miles will it go in 1.7 hours?

10. Fabric costs $6.83 per yard. How much will 3 yards cost?

CH AL L ENGE Solve. 11. A baker packs 2 dozen cookies in each box. If each cookie costs $1.25, how much will the box cost?

Level E

| Chapter 12 - 7

| Lighthouse MATH

247

Solve.

12 - 8 | Chapter Review Solve. 1.

DAILY REV IE W

3.4 × 2.5

6.75 × 1.20

4.80 × 3.25

7.35 × 0.60

2.45 × 4.20

L E T ' S REV I EW Multiplying a Decimal by 10, 100, or 1,000

Multiplying Decimals

Count the zeros and move that many places to the right.

Ignore the decimal point until the end. Then, count the total number of decimal places and put the decimal point in the answer.

5.64 × 1,000 = 5,640

5.26 × 0.03 0.1578

5.640

2 decimal places + 2 decimal places 4 decimal places

Add zeros to any empty spaces.

Rounding to Estimate Products 5.9 × 7.2

Round each number. Multiply.

6 7 42

AP P LY Multiply. 1.

3.4 × 6

2.18 × 7

6.3 × 5

1.72 × 4

4.61 × 8

3.24 × 0.005

6.13 × 0.04

2.41 × 0.003

4.8 × 0.5

10.

7.35 × 0.08

248

Level E

| Chapter 12 - 8

| Lighthouse MATH

Exercise | 12 - 8 Name

Multiply. 1.

2.34 × 4.12

3.42 × 5.6

2.13 × 4.2

6.34 × 3.25

1.72 × 7.48

4.61 × 2.8

3.248 × 4.75

5.06 × 3.21

2.47 × 5.63

10.

4.06 × 3.25

11.

7.72 × 1.48

12.

2.18 × 4.7

13.

3.46 × 2.8

14.

6.35 × 2.84

15.

5.24 × 1.75

16. A notebook costs $2.45. Emma buys 3 notebooks. How much money does she spend?

17. A cup of milk contains 12.35 grams of sugar. How much sugar is in 3.1 cups of milk?

18. A bag of chips weighs 6.81 ounces. How much do 12 bags of chips weigh?

19. A pack of markers costs $3.60. Lisa buys 4 packs. How much money does she spend?

Level E

| Chapter 12 - 8

| Lighthouse MATH

249

Read the problem. Then solve.

12 - 9 | Cumulative Review

Solve. 1.

8 + 6

6 × 5

7 × 9

13 − 9

6 + 8

9 + 8

13 − 5

8 − 3

9 × 7

10.

4 − 2

11.

4 × 6

12.

2 × 7

13.

8 − 4

14.

3 × 7

15.

7 × 6

16.

9 − 5

17.

5 + 4

18.

2 + 9

19.

10 − 3

20.

8 × 3

21.

7 − 1

22.

8 + 4

23.

2 + 4

24.

9 + 6

25.

6 + 5

26.

8 × 9

27.

1 + 5

28.

12 − 7

29.

4 × 7

30.

12 − 3

31.

16 − 8

32.

5 + 5

33.

1 + 9

34.

1 × 5

35.

6 × 8

36.

3 × 1

37. 9 27

38. 4 24

39. 9 18

40. 1 5

41. 3 6

42. 7 35

43. 6 6

44. 4 28

45. 6 30

46. 3 18

47. 7 49

48. 2 12

49. 6 54

50. 5 45

51. 9 36

52. 1 4

53. 6 18

54. 3 15

250

Level E

| Chapter 12 - 9

| Lighthouse MATH

Exercise | 12 - 9 Name

Add. 1.

987 + 951

663 + 356

802 + 238

8,463 + 2,806

5,033 + 8,336

639 − 349

572 − 488

4,241 − 2,557

10.

8,273 − 2,472

12.

689 × 6

13.

5,969 × 6

14.

4,096 × 2

15.

10 × 39

Subtract. 6.

529 − 402

Multiply. 11.

213 × 4

Divide. 17. 2 167

18. 3 917

19. 4 1,461

20. 27 1,053

16. 2 143

Compare using <, >, or =. 21. 3.9

4.9

22. 2.94

2.85

23. 3.00

3.0

24. 0.78

0.87

25. 6.45

6.04

26. 0.9

0.09

27. 14.07

14.7

28. 9.5

9.50

29. 3.765

3.675

30. 1.003

1.03

31. 0.240

0.24

32. 1.06

0.06

Level E

| Chapter 12 - 9

| Lighthouse MATH

251

13 C H A P T E R

252

In Chapter 13, we will learn about

Dividing Decimals We can divide decimals just like whole numbers. Follow simple rules to find the quotient. • We will learn a trick to divide by 10, 100, or 1,000. • We will divide a decimal by a whole number. • We will divide with zeros in the quotient. • We will divide money amounts. • We will solve real-world problems.

253

13 - 1 | Dividing a Decimal by 10, 100, or 1,000 Solve. 1.

DAILY REV IE W

431 × 10

85 × 100

3 × 1,000

98 × 1,000

L E A R N A ND C ONNEC T

To divide a decimal by 10, 100, or 1,000, move the decimal point to the left. Add zeros to any empty spaces. 45.67 ÷ 10

45.67 ÷ 100

45.67 ÷ 1,000

There is 1 zero in 10 so we move the decimal point 1 place to the left.

There are 2 zeros in 100 so we move the decimal point 2 places to the left.

There are 3 zeros in 1,000 so we move the decimal point 3 places to the left.

45.67

045.67

4.567

0.4567

0.04567

AP P LY Divide. 1. 73 ÷ 10

2. 5.8 ÷ 100

3. 612.9 ÷ 1,000

4. 48.25 ÷ 100

5. 39.4 ÷ 100

6. 145.8 ÷ 10

7. 4.23 ÷ 1,000

8. 62.1 ÷ 100

254

Level E

| Chapter 13 - 1

| Lighthouse MATH

Exercise | 13 - 1 Name

Divide. 1. 347 ÷ 10

2. 347 ÷ 100

3. 347 ÷ 1,000

4. 9.6 ÷ 100

5. 825.3 ÷ 1,000

6. 17.52 ÷ 10

7. 6.4 ÷ 10

8. 46 ÷ 100

9. 58.9 ÷ 1,000

10. 2.75 ÷ 10

11. 910.4 ÷ 10

12. 66.4 ÷ 100

13. 7.3 ÷ 10

14. 145 ÷ 1,000

15. 30.5 ÷ 10

16. 88.2 ÷ 100

17. 97.3 ÷ 100

18. 987 ÷ 100

19. 825.7 ÷ 10

20. 4.2 ÷ 100

21. 3.7 ÷ 10

22. 77.3 ÷ 1,000

23. 709 ÷ 10

24. 40.2 ÷ 100

25. Jacob has 4.19 feet of ribbon. He wants to share it equally with 10 friends. How much ribbon does each person get?

Read the problem. Then solve. 26. A farmer sorts 53.9 pounds of vegetables into 100 crates. How many pounds of vegetables will go in each crate?

CH AL L ENGE 27. Riverpark School made $5,044.45 at a sale. They divide the money equally among 100 student clubs. About how much money will each club get?

Level E

| Chapter 13 - 1

| Lighthouse MATH

255

13 - 2 | Dividing a Decimal by a Whole Number Solve. 2. 657 ÷ 100

1. 34.9 ÷ 10

DAILY REV IE W

3. 908.1 ÷ 100

4. 9.6 ÷ 1,000

L E A R N A ND C ONNEC T David cuts a 3.75-inch-long rope into 5 equal pieces. What is the length of each piece? To find the length of each piece, divide by .

Bring up the decimal point. . 5 3.75

Decide where to start dividing. Put a zero above the place you cannot divide.

Follow the steps for long division.

0. 5 3.75

0.75 5 3.75 − 35 25 − 25 0

5 does not fit into 3. 5 can fit into 37

Remember:

☑ ☑

Divide Multiply Subtract Bring down

AP P LY Divide. 1.

8 6 4 8 − −

5 3 1 5 − −

7 9 6 6 − − −

256

Level E

| Chapter 13 - 2

| Lighthouse MATH

4 2 3 6 − −

Exercise | 13 - 2 Name

Divide. 1.

3 1.86

6 212.4

5 25.15

3 54.3

8 64.8

6 548.4

5 43.5

3 4.8

10. 4 25.6

4 8.68

Rewrite and solve. 12. 672.8 ÷ 8

13. 483.6 ÷ 6

14. 904.75 ÷ 5

15. 183.9 ÷ 3

16. 628.4 ÷ 4

17. 306.72 ÷ 9

18. 215.6 ÷ 4

11. 84.36 ÷ 4

CH AL L ENGE Fill in the missing digit to make this division true. 19.

6. 5 7 46. 6

Level E

| Chapter 13 - 2

| Lighthouse MATH

257

13 - 3 | Dividing a Decimal with Zeros in the Quotient Solve. DAILY REV IE W

1. 3 96.36

2. 4 72.48

3. 5 125.5

4. 8 48.64

L E A R N A ND C ONNEC T Ella has 0.25 of a gallon of red paint. She splits it into 5 small cups. Each cup gets the same amount. How much paint is in each cup? To find the amount of paint, divide

Bring up the decimal point.

Decide where to start dividing. Put a zero above the place you cannot divide.

Divide.

. 5 0.25

0.0 5 0.25

0.05 5 0.25 − 25 0

5 doesn’t fit into 0 or 2. 5 can fit into 25

Each cup gets 0.05 gallons of paint.

AP P LY Divide. 1.

6 0 4 8 −

5 0 3 5 −

8 1 0 4 − −

8 0 6 4 −

2 2 0 8 −

−

258

Level E

| Chapter 13 - 3

2 8 0 4 − −

| Lighthouse MATH

Exercise | 13 - 3 Name

Divide. 1.

5 25.05

9 9.36

7 14.07

6 0.18

2 0.02

11 0.55

12 0.36

3 0.06

10. 8 0.56

9 0.81

Rewrite and solve. 12. 0.54 ÷ 9

13. 18.24 ÷ 3

14. 0.48 ÷ 12

15. 0.04 ÷ 4

16. 10.05 ÷ 5

17. 2.08 ÷ 2

18. 4.08 ÷ 4

11. 0.12 ÷ 4

CH AL L ENGE Solve. 19. 2.0048 ÷ 16 =

Level E

| Chapter 13 - 3

| Lighthouse MATH

259

13 - 4 | Dividing Money Solve. DAILY REV IE W

3 0.03

4 8.04

5 3.35

8 40.08

L E A R N A ND C ONNEC T How much will each person get if $11.12 is split 4 ways? To find the amount, divide by .

Bring up the decimal point.

Divide.

Add the dollar sign.

. 4 11.12

2.78 4 11.12 − 8 31 − 28 32 − 32 0

$2.78

Each person gets $2.78.

AP P LY Divide. 1.

260

6 $ 4 2 1 2 −

5 $ 5 0 5 −

8 $ 0 7 2 −

8 $ 1 4 6 4 −

−

Level E

| Chapter 13 - 4

| Lighthouse MATH

Exercise | 13 - 4 Name

Divide. 1.

4 $24.36

5 $45.15

8 $72.48

9 $18.54

12 $0.84

9 $0.45

5 $100.05

18 $2.16

10. 4 $0.08

5 $10.20

Rewrite and solve. 12. $0.96 ÷ 12

13. $13.20 ÷ 8

14. $2.12 ÷ 4

15. $10.08 ÷ 9

16. $1.50 ÷ 6

17. $0.09 ÷ 3

18. $25.60 ÷ 20

11. $50.10 ÷ 5

CH AL L ENGE Fill in the missing number. 19. $1,600.56 ÷

= $200.07

Level E

| Chapter 13 - 4

| Lighthouse MATH

261

13 - 5 | Division Word Problems Solve. DAILY REV IE W

5 $30.15

8 $16.40

3 $21.09

12 $24.96

L E A R N A ND C ONNEC T Andy has 4.84 cups of sugar to split among 4 bowls. Each bowl gets the same amount. How much sugar is in each bowl? We need to divide the cups of sugar by the number of bowls. How many cups of sugar are there? How many bowls will they be split between?

1.21 4 4.84 − 4 08 − 8 04 − 4 0

Each bowl will have 1.21 cups of sugar.

AP P LY Read the problem. Then solve. 1. A piece of ribbon is 4.16 inches long. It is cut into 4 pieces. How long is each piece?

2. A jug holds 5.25 gallons of water. If Sam pours it evenly among 3 buckets, how much will each get?

inches

262

gallons

4 4 1 6 −

3 5 2 5 −

−

Level E

| Chapter 13 - 5

| Lighthouse MATH

Exercise | 13 - 5 Name

1. The temperature in the desert went up 12.9 degrees in 3 hours. How many degrees did it go up each hour?

2. It took a snail 9 hours to travel 0.45 yards. How many yards did it travel per hour?

3. It costs $28.75 for 5 pounds of chicken. How much is it for one pound?

4. A faucet dripped 6.03 gallons of water in 3 hours. How much did it drip each hour?

5. 5.64 inches of snow fell in 6 hours. How many inches fell in one hour?

6. A jug holds 10.89 gallons of water. If it is divided equally between 9 bottles, how much will each bottle hold?

7. A sunflower grew 13.2 inches in 4 days. How many inches did the sunflower grow each day?

8. A dinner costs $12.68. If the cost is split between 2 people, how much will each person pay?

CH AL L ENGE Read the problem. Then solve. 9. Ben and his brother went out for dessert. They got a piece of pie for $4.45, a piece of cake for $5.62, and a donut for $2.27. If they split the bill equally, how much does each brother owe?

Level E

| Chapter 13 - 5

| Lighthouse MATH

263

Read the problem. Then solve.

13 - 6 | Chapter Review Solve. DAILY REV IE W

1. 2 4.8

3 7.2

3. 5 9.45

4. 4 6.36

L E T ' S REV I EW

Dividing Decimals

Dividing by 10, 100, or 1,000

Place the decimal point.

Follow the steps for long division.

. 7 84.42

12.06 7 84.42 − 7 14 − 14 04 − 0 42 − 42 0

Count the number of zeros in the divisor. Move the decimal point to the left that many places. Add zeros to empty places.

14.56 ÷ 1,000 = 0.01456

AP P LY Divide. 1. 658 ÷ 10

2. 87 ÷ 100

3. 2 ÷ 1,000

4. 3.4 ÷ 100

5. 5.478 ÷ 1,000

6. 84.25 ÷ 10

7. 0.3 ÷ 10

8. 5.23 ÷ 100

10. 854.7 ÷ 10

11. 852.36 ÷ 100

12. 84.6 ÷ 100

264

236.8 ÷ 1,000

Level E

| Chapter 13 - 6

| Lighthouse MATH

Exercise | 13 - 6 Name

Divide. 1.

4 104.4

6 80.64

5 31.25

8 108.48

11 99.11

12 36.96

15 105.30

17 102.68

10. 13 65.91

3 56.82

Rewrite and solve. 12. 144.72 ÷ 8

13. 160.64 ÷ 16

14. 130.91 ÷ 13

Read the problem. Then solve. 15. A bake sale raises $245.50. The money is split equally among 5 groups. How much money does each group get?

16. A recipe uses 312.75 ounces of sugar to make 5 cakes. How much sugar goes into each cake?

17. There are 420.84 pounds of apples. The apples are split equally into 4 boxes. What is the weight of each box?

18. A bake sale made $275.25 selling cupcakes. The money is shared equally among 5 classes. How much money does each class get?

Level E

| Chapter 13 - 6

| Lighthouse MATH

265

11. 72.18 ÷ 9

13 - 7 | Cumulative Review

Solve. 1.

4 + 8

2 × 5

7 × 5

4 × 3

1 + 2

5 + 7

5 + 1

6 + 9

8 + 2

10.

8 − 5

11.

8 × 5

12.

10 − 3

13.

5 × 7

14.

15 − 9

15.

11 − 3

16.

4 − 1

17.

10 − 5

18.

1 × 7

19.

6 + 1

20.

3 + 7

21.

6 + 6

22.

12 − 5

23.

10 − 6

24.

3 × 7

25.

4 + 3

26.

9 + 7

27.

7 − 2

28.

4 + 9

29.

4 + 7

30.

6 − 1

31.

4 × 5

32.

7 + 8

33.

9 + 8

34.

3 + 8

35.

7 − 5

36.

1 × 2

37. 4 12

38. 4 4

39. 3 27

40. 8 8

41. 3 3

42. 1 2

43. 6 48

44. 5 40

45. 1 6

46. 2 12

47. 9 18

48. 7 42

49. 9 63

50. 3 12

51. 7 28

52. 6 12

53. 5 35

54. 8 64

266

Level E

| Chapter 13 - 7

| Lighthouse MATH

Exercise | 13 - 7 Name

Add. 1.

90.3 + 67.1

7.63 + 3.06

612 + 533

1.091 + 5.933

0.3892 + 0.6363

705 − 579

6.57 − 3.98

4.451 − 0.366

10.

6,731 − 4,911

12.

72.6 × 1

13.

9.116 × 9

14.

9,925 × 1

15.

8.7 × 2.6

Subtract. 6.

43.1 − 16.3

Multiply. 11.

7.80 × 8

16. 8 56.8

17. 8 57.6

18. 2 1.852

19. 4 416

20. 83 1.577

23. 63.58

24. 105.003

25. 64.607

28. 1.471

29. 4.564

30. 9.869

Divide.

Round to the nearest whole number. 21. 658.23

22. 4.89

Round to the nearest hundredth. 26. 2.788

27. 3.695

Level E

| Chapter 13 - 7

| Lighthouse MATH

267

14 C H A P T E R

268

In Chapter 14, we will learn about

The Coordinate Plane When we collect numbers in the world around us, we are collecting data. We can look for patterns in the data to help us plan for the future. • We will find the rules to patterns and use the rule to predict what comes next. • We will use a rule to make a table. • We will learn to read a grid map. • We will learn about the coordinate plane. • We will graph ordered pairs. • We will graph from a table.

269

14 - 1 | Patterns Solve. DAILY REV IE W

8+5=

37 − 4 =

12 + 8 =

21 − 9 =

L E A R N A ND C ONNEC T When numbers, shapes, or objects grow or shrink in a set way, they make a pattern. We can find and use the rule for the pattern to predict what comes next. Look at the pattern.

Find the rule. Look at how the pattern changes.

25, 45, 65

Use the rule to find what comes next.

25, 45, 65

25, 45, 65, 85

+ 20 + 20

+ 20

AP P LY Use the rule to continue the pattern. 1. Rule: Add 3 2, 5, 8,

2. Rule: Subtract 6 30, 24, 18,

4. Rule: Subtract 10

5. Rule: Add 4

100, 90, 80,

15, 19, 23,

7. Rule: Add 2 13, 15,

270

3. Rule: Add 5 ,

21,

Level E

, 31

, 157, 156, 155, 154 9. Rule: Subtract 5

, 35, 42, 49

| Chapter 14 - 1

6. Rule: Subtract 1

8. Rule: Add 7

, 19, 21

5, 10, 15,

| Lighthouse MATH

32, 27,

, 17, 12,

Exercise | 14 - 1 Name

Draw the next figure in the pattern. 1.

*^^*^^

Find the rule and the missing numbers in the pattern. 6. 4, 6, 8,

7. 37, 43, 49,

Rule:

9. 4, 11,

Rule:

10.

, 25, 32

Rule:

8. 77, 66, 55,

Rule:

, 42, 39, 36, 33

Rule:

11. 13, 25,

, 49, 61

Rule:

Read the problem. Then solve. 13. A tank has 32 inches of water. After one hour, it has 62 inches. After two hours, it has 92 inches. If this pattern continues, how many inches of water will there be after three hours?

12. On Monday, 12 flowers bloom. On Tuesday, 16 flowers bloom. On Wednesday, 20 flowers bloom. If this pattern continues, how many flowers will bloom on Friday?

CH AL L ENGE Find the next two numbers in each pattern. 14. 17, 21, 25, 29,

15. 2, 4, 7, 11,

Level E

| Chapter 14 - 1

| Lighthouse MATH

16. 2, 4, 8, 16,

271

14 - 2 | Using a Rule to Make a Table Find the rule and the next number. 1. 1, 3, 5,

DAILY REV IE W

2. 10, 17, 24,

3. 99, 77, 55,

Rule:

L E A R N A ND C ONNEC T Fanny puts red and white flowers in a vase. She always puts in 3 more red than white. We can use an x-y table to show the number of red flowers for any number of white flowers.

Add 3 to the number of white flowers to find the number of red flowers. x (white flowers)

+3 y (red flowers)

3 +3

AP P LY Use the rule to complete the table. 1. Add 4 to x to find y.

2. Multiply x by 2 to find y.

3. Subtract 3 from x to find y.

272

Level E

4. Subtract 6 from x to find y. 13

| Chapter 14 - 2

| Lighthouse MATH

Exercise | 14 - 2 Name

Use the rule to complete the table. 2. Multiply x by 8 to find y.

1. Add 5 to x to find y. 12

4. Subtract 9 from x to find y.

5. Multiply x by 3 to find y. x

3. Subtract 12 from x to find y. x

6. Add 4 to x to find y. x

7. Subtract 2 from x to find y.

8. Multiply x by 5 to find y.

Use the rule to complete the table. 9. A factory makes bolts and screws. The number of bolts made is always 25 less than the number of screws. Fill in the chart with x as the number of screws and y as the number of bolts.

x (screws)

100

y (bolts)

CH AL L ENGE Use the rule to complete the table.

10. Rule: Multiply x by 2 and then add 4 to find y.

Level E

| Chapter 14 - 2

| Lighthouse MATH

273

14 - 3 | Reading a Grid Map Use the rule to complete the table. DAILY REV IE W

Add 10 to x to find y.

L E A R N A ND C ONNEC T A map shows the location of objects or places. We can write the exact location with a coordinate point. Write the coordinate point that shows the location of the park. Start at 0. Move your finger to the right until it is under the park. Count the number of spaces.

Move up until you reach the park. Count the number of spaces.

5 4 3 2 1

( 5 , 4 )

AP P LY Start at 0. Count the number of spaces to the right and up until you get to the object. 12 11 10 9

right

8 7 6

(

)

(

)

(

)

(

)

(

)

(

)

5 4 3 2 1 0

274

9 10 11 12 13 14

Level E

| Chapter 14 - 3

| Lighthouse MATH

Exercise | 14 - 3 Name

Use the grid map to answer the questions. 1.

Where is the rainbow? (

Where is the umbrella? (

) ,

)

How many units is the sun away from the star?

5 4

How would you get from the umbrella to the moon?

3 2 1

Where is the monkey? (

Where is the lion? (

) )

How many units is the zebra from the fish?

5 4

How would you get from the zebra to the lion?

Start at the moon. Move right 4 units and up 2 units. Where are you?

2 1 0

Start at the monkey. Move right 7 units and up 1 unit. Where are you?

CH AL L ENGE Read the problem. Then solve. 3. A fire engine is located at (1, 2). It moves to the left 1 unit and up 3 units. Where is it located now?

Level E

| Chapter 14 - 3

| Lighthouse MATH

275

14 - 4 | The Coordinate Plane Answer the question using the grid map below. 1.

DAILY REV IE W

How would you get from the apple to the tree?

1 0

L E A R N A ND C ONNEC T A coordinate plane is a grid with two number lines that cross. A point is a specific spot on the grid. We describe its location using two numbers: one from the x-axis and one from the y-axis.

y-axis Vertical number line

Origin (0, 0) Point where the axes meet

Coordinate point

10 9 8 7 6 5 4 3 2 1

(4, 6) x - coordinate (x ,y), shows the horizontal location

y - coordinate (x ,y), shows the vertical location

x-axis Horizontal number line

1 2 3 4 5 6 7 8 9 10

AP P LY Find each point on the coordinate plane. 1.

To find the point: • Put your finger on the origin (0,0).

A (

)

•

M (

)

Move right and count until your finger is lined up with the point.

•

Move up and count until your finger touches the point.

•

Write the point as: (the amount right, the amount up).

C (

)

L (

)

E (

)

Vocabulary Coordinate plane - grid made from intersecting horizontal and vertical axes Origin - starting point with (0,0) coordinates x-axis - horizontal line of the coordinate plane y-axis - vertical line of the coordinate plane

276

Level E

| Chapter 14 - 4

| Lighthouse MATH

A 12 11 G E 10 R 9 M D 8 H 7 O Q 6 C 5 F B 4 L 3 P 2 N J 1 K 0 1 2 3 4 5 6 7 8 9 10 11 12

Exercise | 14 - 4 Name

Find each point on the coordinate plane. Write the letter of each point. 1.

10 9 H

8 W

7 6

Q J M C D

2 1 0

(7, 8)

(8, 7)

(3, 7)

(5, 5)

(1, 4)

(8, 2)

(3, 1)

(5, 0)

(4, 2)

(1, 3)

(4, 1)

5 4

(0, 6)

R 1

Write the coordinates of each point. 2.

10 N

9 P

7 R

D Z

N (

)

A (

)

D (

)

Z (

)

M (

)

T (

)

B (

)

3 F

T B

1 0

)

F (

CH AL L ENGE Read the problem. Then solve. 3. Point A is (2, 2). Point B is (2, 7). How far apart are Point A and Point B?

Level E

| Chapter 14 - 4

| Lighthouse MATH

277

14 - 5 | Graphing Ordered Pairs Put a circle around the x-coordinate. Put a square around the y-coordinate. DAILY REV IE W

(5, 9)

(1, 4)

(0, 6)

(2, 0)

L E A R N A ND C ONNEC T We use a coordinate point to plot a dot on a coordinate plane. The x-coordinate (x, y) tells us how far to move right. The y-coordinate (x, y) tells us how far to move up. Draw a dot to plot the point. Plot the point (5, 3). 6

Start at the origin (0,0). Move right to find the x-coordinate on the x-axis. Stay on the line. Move up to the y-coordinate on the y-axis.

5 4

(5, 3)

3 2 1

Draw a dot on the coordinate plane.

AP P LY Follow the directions to plot the points on the coordinate plane. 1.

(4, 3) Start at the origin (0,0). Find the 4 on the x-axis. Move up to the 3 on the y-axis. Put a dot at the point (4, 3).

8 7 6 5 4

(6, 1) Start at the origin (0, 0). on the x-axis. Find the Move up to the on the y-axis. Put a dot at the point (6, 1).

3 2 1 0

Vocabulary Coordinate point - an exact spot on the coordinate plane x-coordinate - the x value of the coordinate point y-coordinate - the y value of the coordinate point

278

Level E

x-axis - horizontal line of the coordinate plane y-axis - vertical line of the coordinate plane Plot - to place a point on a plane or grid

| Chapter 14 - 5

| Lighthouse MATH

Exercise | 14 - 5 Name

Plot each point. Connect the dots. Write the name of the shape you made. (1, 1) (1, 5) (5, 5) (5, 1)

7 6

(2, 4) (4, 6) (6, 4) (4, 2)

(0, 7) (6, 7) (4, 2)

8 7 6 5

1 1

8 7 6 5

(1, 2) (5, 2) (7, 5) (3, 5)

1 4

8 7 6 5

(1, 3) (1, 5) (5, 3) (5, 5)

1 4

(2, 0) (2, 4) (6, 0)

CH AL L ENGE Read the problem. Then solve. 7. How many units are there between (2, 2) and (8, 2)?

Level E

| Chapter 14 - 5

| Lighthouse MATH

279

14 - 6 | Graphing from a Table Plot each point. Connect the dots. Write the name of the shape you made. 1. DAILY REV IE W

(1, 1) (1, 4) (4, 1) (4, 4)

5 4 3 2 1 0

1 2 3 4 5

L E A R N A ND C ONNEC T We can graph a pattern shown in a table on the coordinate plane. Write a list of ordered pairs and plot them on the graph. When a coordinate plane shows a real-life situation, the x-axis and y-axis are labeled. Table

Ordered Pairs

Coordinate Plane How Bamboo Grows 8

x- number of days

y - height (in inches)

(0, 1) (1, 3) (2, 5) (3, 7)

7 Height (in inches)

How Bamboo Grows

6 5 4 3 2 1 0

2 3 4 5 6 7 Number of days

AP P LY Plot the points from the table on the coordinate plane. Then answer the questions. 1.

x- number of days

y- money Sam has

Money in Sam’s Wallet

Money Sam has ($)

After 2 days, the bamboo is 5 inches tall.

8 7 6 5 4 3 2 1 0

After 1 day, how much money does Sam have? After 3 days, how much money does Sam have?

1 2 3 4 5 6 7 8

After how many days will Sam have $6?

Number of days

280

Level E

| Chapter 14 - 6

| Lighthouse MATH

Exercise | 14 - 6 Name

Plot the points from the table on the coordinate plane. Then answer the questions. x- cups of flour

y- loaves of bread

Baking Bread

Loaves of bread

8 7 6 5 4 3 2 1 0

If the baker has 4 cups of flour, how many loaves can he make?

If the baker has 1 cup of flour, how many loaves can he make? 1 2 3 4 5 6 7 8 Cups of flour

Cost of Ice Cream

x- number y- total cost of toppings 0

Total cost ($)

8 7 6 5 4 3 2 1 0

How much flour is needed for 4 loaves of bread?

How much does it cost to get 2 toppings? How much does it cost to get 4 toppings?

1 2 3 4 5 6 7 8

How many toppings do you get if you spend $8?

Number of toppings

y- gallons of gas left

Gas in the Tank 8 7 6 5 4 3 2 1 0

After 1 hour, how many gallons of gas are left? After 3 hours, how many gallons of gas are left?

1 2 3 4 5 6 7 8

x- hours passed

Gallons left

After how many hours will the car have 6 gallons of gas?

Hours passed

CH AL L ENGE Make a table to match the story. 4. A slug is moving across a garden path. It travels 2 feet every hour.

Level E

| Chapter 14 - 6

| Lighthouse MATH

281

14 - 7 | Chapter Review Use the table to answer the question. 1.

DAILY REV IE W

x- desks

How many chairs are needed for ...

y- chairs

2 desks?

4 desks?

L E T ' S REV I EW Patterns, Rules, and Tables

Coordinate Plane

Some tables show patterns and rules.

A coordinate point has two numbers. The x-coordinate tells the number on the x-axis. The y-coordinate tells the number on the y-axis.

We can multiply x by 3 to find y.

(1, 3)

×3

(2, 6)

y-axis

(0, 0)

(3, 9)

9 8 7 6 5 4 3 2 1 0

1 2 3 4 5 6 7 8 9 x-axis

AP P LY Find the rule and the next number in the pattern. 1.

4, 7, 10, Rule:

9, 7, 5, Rule:

1, 3, 5,

81, 91, 101,

Rule:

Use the rule to complete the table. 5.

282

Add 5 to x to find y. x

Level E

Add 8 to x to find y. x

| Chapter 14 - 7

| Lighthouse MATH

Multiply x by 5 to find y. x

Exercise | 14 - 7 Name

Use the grid to answer the questions. 1.

7 6 5

Write the coordinates.

)

Write the points.

1 0

H 4

(7, 5)

(4, 0)

(0, 5)

(4, 5)

Plot each point. Connect the dots. Write the name of the shape you made. (2, 6) (6, 6) (6, 2) (2, 2)

8 7 6 5

(1, 5) (2, 8) (5, 8) (4, 5)

8 7 6 5

CH AL L ENGE Plot the points from the table on the coordinate plane. Answer the questions. Mannie’s Money

x- weeks

y- dollars saved

How much money did Mannie save after 1 week? How much money did Mannie save after 3 weeks?

6 Dollars Saved

5 4

How many weeks did it take Mannie to save $4?

3 2 1 0

Weeks

Level E

| Chapter 14 - 7

| Lighthouse MATH

283

14 - 8 | Cumulative Review

Solve. 1.

6 × 6

15 − 8

11 − 9

2 + 5

17 − 8

2 × 7

7 − 1

2 + 2

4 + 2

10.

6 × 8

11.

8 × 9

12.

3 + 4

13.

3 × 6

14.

15 − 7

15.

5 × 2

16.

10 − 6

17.

4 × 8

18.

11 − 4

19.

1 × 4

20.

7 − 3

21.

7 − 6

22.

7 + 6

23.

11 − 7

24.

4 × 6

25.

5 × 5

26.

6 + 5

27.

1 × 9

28.

9 − 1

29.

3 + 1

30.

7 + 5

31.

10 − 1

32.

6 × 1

33.

5 + 4

34.

5 × 7

35.

6 + 4

36.

8 + 5

37. 6 30

38. 3 6

39. 2 14

40. 4 28

41. 4 8

42. 6 36

43. 3 9

44. 5 35

45. 4 16

46. 2 16

47. 2 12

48. 9 18

49. 5 30

50. 9 72

51. 3 12

52. 5 10

53. 8 48

54. 6 54

284

Level E

| Chapter 14 - 8

| Lighthouse MATH

Exercise | 14 - 8 Name

Add. 1.

57.9 + 51.2

6.09 + 8.83

0.967 + 0.789

1,226 + 3,908

81.60 + 35.17

7.72 − 3.69

0.320 − 0.157

93.60 − 17.24

10.

9,655 − 8,478

12.

3.4 × 6

13.

2.13 × 1.94

14.

0.08 × 0.6

15.

4.25 × 3

Subtract. 6.

47.5 − 23.2

Multiply. 11.

0.005 × 7

Divide. 17. 2 9.2

18. 6 301.8

19. 5 19.95

20. 23 1.265

16. 8 3.36

Write the fractions as decimals. 3

21. 4

22. 10

23. 5

24. 2

25. 20

Write the decimals as fractions in simplest form. 26. 0.3

27. 0.25

Level E

28. 0.48

| Chapter 14 - 8

| Lighthouse MATH

29. 0.16

285

15 C H A P T E R

286

In Chapter 15, we will learn about

Geometry and Measurement We can find math in the world around us when we look at and measure objects. It's important to understand the units of measure so that we can find the size of an object. • We will categorize angles and lines. • We will identify 3D shapes. • We will find perimeter and area of different shapes. • We will learn how to find the volume of a rectangular prism. • We will convert units of time. • We will convert units of length. • We will convert units of weight and capacity.

287

15 - 1 | Angles and Lines Plot the points from the table on the coordinate plane. 1. DAILY REV IE W

x (number of rows)

y (number of plants)

6 5 4 3 2 1 0

1 2 3 4 5 6

L E A R N A ND C ONNEC T We can label two lines by how they cross. Angles are formed when two lines cross. We measure the space between the two lines in degrees (°).

Angles

Lines

Acute

Obtuse

less than 90°

greater than 90°

Right

Straight

90°

180°

Parallel

Intersecting

Perpendicular

AP P LY Label each set of lines as intersecting, parallel, or perpendicular. 1.

Vocabulary Angle - a figure formed by two rays that are connected at a vertex Intersecting lines - two lines that cross Parallel lines - two lines that will never intersect Perpendicular lines - two lines that intersect at a right angle

288

Level E

Right angle - a 90º angle Straight angle - a 180º angle Acute angle - an angle with a measure less than 90º Obtuse angle - an angle with a measure greater than 90º and less than 180º

| Chapter 15 - 1

| Lighthouse MATH

Exercise | 15 - 1 Name

Label each angle as acute, right, obtuse, or straight. H

3. Q

C G

7. Q

8. R

10.

11.

12.

Label each set of lines as intersecting, parallel, or perpendicular. 14.

15.

13.

CH AL L ENGE A

Write acute, obtuse, right, or straight for each of the angles below. 16.

BCA

EDG

LMN

GIK

Level E

| Chapter 15 - 1

| Lighthouse MATH

289

15 - 2 | Classifying 3D Figures Name the figures. 1.

DAILY REV IE W

L E A R N A ND C ONNEC T 2D shapes are flat. 3D shapes are solid. Below are some 3D shapes and their names. 3D Figures

Rectangular prism

Triangular prism

Rectangular pyramid

Cylinder

Triangular pyramid

Cone

Sphere

AP P LY Write the name of each figure. 1.

Vocabulary 3D Figure - a solid shape that has three dimensions

290

Level E

| Chapter 15 - 2

| Lighthouse MATH

Exercise | 15 - 2 Name

10.

11.

12.

Name the solid figures.

CH AL L ENGE Name all of the 3D shapes in the picture. 13.

Level E

| Chapter 15 - 2

| Lighthouse MATH

291

15 - 3 | Perimeter Find the value of each expression. DAILY REV IE W

(2 × 8) + (2 × 3) =

100 + 30 + 100 + 30 =

8×4=

L E A R N A ND C ONNEC T The perimeter is the distance around a shape. To find the perimeter of a shape, add up all the sides. How much fencing is needed for the field? 4 yards

5 yards

4 + 4 + 5 + 5 = 18 yards of fencing

5 yards

4 yards

AP P LY

Find the perimeter. 1.

2. 7 cm

5 ft

10 cm

3 cm

+ 3.

2 units

1 in

2 units 2 units

4 units

2 units 4 units

Vocabulary Perimeter - the distance around a shape

292

Level E

| Chapter 15 - 3

| Lighthouse MATH

units

Exercise | 15 - 3 Name

Find the perimeter. 1.

2. 8m

3. 3 ft

12 in

3 ft

4 cm

3 ft

4. 10 cm

17 in

10 cm

12 in

3 in

3 cm

2 cm

2 in

10 cm

8. 3 in

5 cm 7 cm

2 cm 2 cm

8 ft 4 in

4 cm

Read the problem. Then solve. Draw a picture to help. 10. A square rug in a classroom has a side that is 5 feet long. What is the perimeter of the rug? Hint: A square has four equal sides.

9. A rectangular garden is 6 feet long and 4 feet wide. If you walk around the edges, how far will you walk?

CH AL L ENGE Find the missing side length. 11. The total perimeter of a triangle is 15 inches. One side is 5 inches, and another side is 4 inches. How long is the third side?

Level E

| Chapter 15 - 3

| Lighthouse MATH

293

15 - 4 | Area Find the perimeter of each shape. 1.

2 ft

DAILY REV IE W

5 cm

7 units

1 cm 6 ft

2 units

6 cm

L E A R N A ND C ONNEC T

2 yards

Area is the amount of space a shape takes up. To find the area of a rectangle, multiply the length by the width.

3 yards

Some shapes can be divided into rectangles to find the area.

3 yards

How many square yards is the field? Divide the shape into rectangles.

5 yards

Add the areas. Label with square units.

Multiply the length by the width to find each area.

2 yd

3 yards × 2 yards = 6 square yards

3 yd

3 yards × 5 yards = 15 square yards

6 square yards 15 square yards 21 square yards

3 yd

Area is measured in square units.

5 yd

AP P LY Find the area.

3 cm

3 in

3 cm

15 in

in ×

294

in =

10 cm

square inches

Level E

| Chapter 15 - 4

cm × cm × cm +

| Lighthouse MATH

cm = cm = cm =

square cm square cm square cm

Exercise | 15 - 4 Name

Find the area. 1.

3. 6 ft

5 in

10 yd

11 in 6 ft 3 yd

6 ft

7 yd 1 yd

2 ft 5 in

5 ft

4 yd

3 ft 4 yd

7 in

Read the problem. Then solve. Draw a picture to help. 8. Rachel has a square rug that has side lengths of 4 ft. How much area does the rug cover? © Lighthouse Curriculum. Copying strictly prohibited.

7. Adam is tiling a floor that is 4 yards wide and 2 yards long. How many square yards of tile does Adam need?

CH AL L ENGE Read the problem. Then solve. 9. A rectangular garden is 10 feet long. It covers a total of 60 square feet. What is the width of the garden?

Level E

| Chapter 15 - 4

| Lighthouse MATH

295

15 - 5 | Volume Find the area of each rectangle or square. 1.

2. 7 ft

DAILY REV IE W

4 ft

3 units

4. 5 ft

6 cm 12 ft

L E A R N A ND C ONNEC T The volume is the amount of space a 3D shape takes up. To find the volume of a rectangular prism, multiply length × width × height. What is the volume of the fish tank in cubic feet?

6 × 2 × 3

height 3 feet

36 cubic feet

length width height 1 cubic foot

width 2 feet

1 ft 1 ft

Volume is measured in cubic units.

length 6 feet

1 ft

AP P LY Count the boxes to find the length, width, and height. Then find the volume. 1.

units3

Vocabulary Volume - the amount of space a 3D shape takes up

296

Level E

| Chapter 15 - 5

| Lighthouse MATH

Exercise | 15 - 5 Name

Find the volume. 1.

6. 6m

5 yd 2 ft

1 ft

5 ft

6m 3 yd

2 yd

1m 2 yd

6 ft 3 ft 12 ft

8 yd

2 yd

1m 1m

Read the problem. Then solve. 10. Anthony has a shed that is 5 feet long, 5 feet wide, and 3 feet deep. What is the volume of the shed?

11. Hannah has a box that is 5 inches on each side. What is the volume of the box in cubic inches?

CH AL L ENGE Read the problem. Then solve. 12. The volume of a rectangular prism is 100 cubic units. Its length is 10 units, and its height is 2 units. What is its width?

297

15 - 6 | Converting Units of Time Find the volume of each rectangular prism. 1.

3 ft

DAILY REV IE W 3 ft

8 ft

4. 5 ft

3 ft

11 ft

2 ft

4 ft

3 ft

4 ft

7 ft

L E A R N A ND C ONNEC T We use a clock to measure seconds, minutes, and hours. We use a calendar to measure days, weeks, months, and years.

Units of Time

1 minute = 60 seconds

How many seconds are 120 minutes?

How many hours are 120 minutes?

To convert to a smaller unit: Multiply

To convert to a bigger unit: Divide

Each minute is 60 seconds.

There are 60 minutes per hour.

120 × 60 = 7,200

120 ÷ 60 = 2

120 minutes = 7,200 seconds

120 minutes = 2 hours

1 hour = 60 minutes 1 day = 24 hours 1 week = 7 days 1 year = 365 days 1 year = 12 months

AP P LY Multiply to convert to a smaller unit of time. 1.

6 hours =

minutes

3 weeks =

days

4 minutes =

weeks

300 seconds =

seconds

Divide to convert to a bigger unit of time. 4.

48 hours =

days

28 days =

Vocabulary Convert - change from one unit to another without changing the value

298

Level E

| Chapter 15 - 6

| Lighthouse MATH

minutes

Exercise | 15 - 6 Name

Convert the times.

3. 5 minutes =

seconds

5. 120 minutes =

hours

7. 3 days =

2. 10 minutes =

minutes

4. 3 hours =

seconds

minutes

6. 540 minutes =

hours

8. 96 hours =

days

9. 10 days =

hours

10. 21 days =

weeks

11. 28 days =

weeks

12. 10 weeks =

days

13. 36 months =

years

14. 2 years =

months

15. 48 months =

years

16. 3 years =

days

17. 730 days =

18. 3,650 days =

years

1. 120 seconds =

Read the problem. Then solve. 20. The month of May has 31 days. How many hours are in the month of May?

19. A cat sleeps for 14 hours every day. How many minutes does the cat sleep for each day?

CH AL L ENGE Read the problem. Then solve. 21. David studies for 1 hour and 45 minutes. How many minutes does he study for?

Level E

| Chapter 15 - 6

| Lighthouse MATH

299

15 - 7 | Converting Length Convert the times. DAILY REV IE W

months

3 years =

2 days =

hours

2 minutes =

seconds

L E A R N A ND C ONNEC T Length tells us how long an object is. We use tools like rulers, yardsticks, or tape measures to measure inches, feet, yards, and miles. How many inches are 6 feet?

How many yards are 6 feet?

To convert to a smaller unit: Multiply

To convert to a bigger unit: Divide

Each foot is 12 inches.

There are 3 feet per yard.

6 × 12 = 72

6÷3=2

6 feet = 72 inches

6 feet = 2 yards

Units of Length 1 inch

1 foot = 12 inches 1 yard = 3 feet 1 yard = 36 inches

1 mile = 5,280 feet 1 mile = 1,760 yards

AP P LY Multiply to convert to a smaller unit of length. 1.

15 yards =

feet

2 miles =

feet

4 feet =

inches

6 feet =

inches

4 miles =

yards

3 yards =

inches

feet

216 inches =

yards

12. 120 inches =

feet

Divide to convert to a bigger unit of length. 7.

108 feet =

10. 3,520 yards =

300

yards

miles

60 inches =

11. 72 feet =

Level E

| Chapter 15 - 7

yards

| Lighthouse MATH

Exercise | 15 - 7 Name

Convert the lengths.

2. 48 inches =

feet

6 feet =

inches

4. 21 feet =

yards

5. 12 yards =

feet

6. 5 yards =

feet

10 yards =

inches

8. 3 yards =

inches

9. 72 inches =

yards

10. 3 miles =

feet

11. 1 mile =

feet

12. 7 miles =

yards

13. 8 yards =

feet

14. 36 yards =

feet

15. 2 miles =

yards

16. 15 feet =

yards

17. 2,640 feet =

mile

18. 120 inches =

19. 24 inches =

feet

20. 9 feet =

feet

yards

1. 144 inches =

Read the problem. Then solve. 21. A tailor needs 15 feet of ribbon. How many yards of ribbon does the tailor need?

22. An electric cable is 24 inches long. How many feet long is the cable?

CH AL L ENGE Read the problem. Then solve. 23. How many inches are equal to 1 mile?

Level E

| Chapter 15 - 7

| Lighthouse MATH

301

15 - 8 | Converting Weight and Capacity Convert the lengths. DAILY REV IE W

11 yards =

20 miles =

8 feet =

L E A R N A ND C ONNEC T Liquid volume tells us how much space a liquid takes up. We use tools like spoons, cups, bottles, and buckets to measure cups, pints, quarts, and gallons.

Units of Capacity 1 fl ounce 1 cup = 8 fl ounces

Weight tells us how heavy something is. We use a scale to measure ounces, pounds, and tons. How many pints are 8 quarts?

1 pint = 2 cups 1 quart = 2 pints

How many gallons are 8 quarts?

1 gallon = 4 quarts

To convert to a smaller unit: Multiply

To convert to a bigger unit: Divide

Each quart is 2 pints.

There are 4 quarts in a gallon.

8 × 2 = 16

8÷4=2

8 quarts = 16 pints

8 quarts = 2 gallons

Units of Weight 1 ounce 1 pound = 16 ounces 1 ton = 2,000 pounds

AP P LY Multiply to convert to a smaller unit of capacity or weight. 1.

5 gallons =

quarts

3 tons =

pounds

8 quarts =

10,000 pounds =

pints

Divide to convert to a bigger unit of capacity or weight. 4.

302

12 pints =

quarts

Level E

80 ounces =

| Chapter 15 - 8

pounds

| Lighthouse MATH

tons

Exercise | 15 - 8 Name

Convert. 1. 4 gallons =

quarts

2. 20 quarts =

gallons

10 pints =

quarts

6 quarts =

pints

8 pints =

cups

6. 24 cups =

pints

2 gallons =

quarts

8. 32 fl oz =

cups

9. 9 gallons =

quarts

10. 40 pints =

quarts

11. 10 gallons =

quarts

12. 4 tons =

pounds

14. 3 pounds =

ounces

pounds

tons

15. 32 ounces =

pounds

16. 15 tons =

17. 160 ounces =

pounds

18. 2 ton =

pounds

13. 6,000 pounds =

Read the problem. Then solve. 19. Andrew is making a recipe that calls for 12 quarts of juice. How many gallons is this?

20. Mr. Miller has a cooler with 4 pounds of ice inside. How many ounces of ice does he have?

CH AL L ENGE Read the problem. Then solve. 21. How many cups are equal to 1 gallon?

Level E

| Chapter 15 - 8

| Lighthouse MATH

303

15 - 9 | Chapter Review Convert the measurements. DAILY REV IE W

2 gal =

20 cups =

16 fl oz =

cups

L E T ' S REV I EW Perimeter

Area

Volume

Add all the side lengths.

Length × Width

Length × Width × Height

Measured in units

Measured in square units

Measured in cubic units

6 cm

P=6+4+6+4 P = 20 cm

3 cm

A=6×4 A = 24 cm2

4 cm

6 cm

V=6×4×3 V = 72 cm3

4 cm

Time

Length

Liquid Capacity

Weight

1 minute = 60 seconds 1 hour = 60 minutes 1 day = 24 hours 1 year = 365 days

1 foot = 12 inches 1 yard = 3 feet 1 mile = 5,280 feet 1 mile = 1,760 yards

1 cup = 8 fluid ounces 1 pint = 2 cups 1 quart = 2 pints 1 gallon = 4 quarts

1 pound = 16 ounces 1 ton = 2,000 pounds

AP P LY Convert. 1.

3 hours =

minutes

7 days =

hours

300 seconds =

4 gallons =

quarts

12 cups =

quarts

15 feet =

4 tons =

pounds

15 feet =

yards

10,000 pounds =

10. 3 miles =

yards

11. 5 minutes =

seconds

| Chapter 15 - 9

| Lighthouse MATH

304

Level E

12. 10 pounds =

minutes

inches

tons

ounces

Exercise | 15 - 9 Name

Write acute, right, obtuse, or straight for each angle. 1.

2. Y

Write intersecting, parallel, or perpendicular for each figure. 4.

10.

11.

Name the solid figures.

Find the perimeter, area, or volume. 12.

13.

14.

9 ft

2 ft

5 ft

6 ft

2 ft 3 ft 7 ft

Perimeter =

Volume =

Level E

| Chapter 15 - 9

Area =

| Lighthouse MATH

305

15 - 10 | Cumulative Review

Solve. 1.

7 × 7

8 + 5

5 + 4

4 × 3

8 − 3

6 + 3

10 − 1

11 − 2

15 − 9

10.

9 − 3

11.

6 − 3

12.

6 + 4

13.

5 × 5

14.

6 + 7

15.

3 × 5

16.

6 × 4

17.

9 × 1

18.

11 − 4

19.

8 × 2

20.

9 × 7

21.

7 − 3

22.

7 − 5

23.

8 − 5

24.

9 + 4

25.

8 × 4

26.

14 − 8

27.

8 + 3

28.

1 × 8

29.

14 − 5

30.

14 − 6

31.

12 − 7

32.

9 − 8

33.

11 − 9

34.

4 × 9

35.

2 + 9

36.

8 − 4

37. 1 8

38. 4 24

39. 6 30

40. 6 48

41. 3 24

42. 7 35

43. 2 2

44. 9 63

45. 8 64

46. 2 18

47. 5 30

48. 4 32

49. 3 21

50. 7 14

51. 8 16

52. 5 15

53. 3 15

54. 3 9

306

Level E

| Chapter 15 - 10

| Lighthouse MATH

Exercise | 15 - 10 Name

Add. 1.

47.9 + 24.6

4.35 + 5.26

0.694 + 0.123

2.958 + 8.976

6,981 + 4,432

663 − 243

720 − 521

7,822 − 4,772

10.

810.5 − 559.9

12.

1.41 × 2

13.

415.8 × 6

14.

19.66 × 0.2

15.

0.59 × 0.72

Subtract. 6.

621 − 431

Multiply. 11.

130 × 9

Divide. 17. 3 123.6

18. 5 96.25

19. 8 63.36

20. 3 36.69

16. 6 45.6

Continue the pattern. 21. 22. 23. 17, 19, 21, 23, 25. 12, 21, 30, 39,

Level E

| Chapter 15 - 10

24. 14, 22, 30, 38,

26. 28, 31, 34, 37,

| Lighthouse MATH

307

www.lighthousecurriculum.com

Mastering Bright Ideas ™

Lighthouse Math Level E 718.285.7100 • info@lighthousecurriculum.com For more information visit www.lighthousecurriculum.com