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Whole Numbers
Unit 1 Numbers to 1,000,000,000
Exercise 1.1 Reading and writing numbers
Coursebook Recap
a) 1,000,000 10,000,000 100,000,000 1,000,000,000 (One million) (Ten million) (One hundred million) (One thousand million)
One thousand million is also known as one billion.
1,000 million = 1,000,000,000 = 1 billion
b) 245,406,815 is read as two hundred and forty-five million, four hundred and six thousand, eight hundred and fifteen.
1. Write the numerals.
a) eight million, sixty-four thousand and twenty
b)twenty-nine million, five hundred and eighty thousand, nine hundred and fifteen
c)seven hundred and sixty million, three hundred and fifty-four thousand and eight hundred
2. Write the numerals in words.
a) 6,405,960 b) 47,618,215
a) 800,307,613
29,580,915 8,064,020 760,354,800
eight hundred million, three hundred and seven thousand, six hundred and thirteen forty-seven million, six hundred and eighteen thousand, two hundred and fifteen six million, four hundred and five thousand, nine hundred and sixty
Exercise 1.2 Identifying values of digits
Coursebook Recap
In 745,600,023, the digit 7 is in the hundred millions place and its value is 700,000,000.
745,600,023 = 700,000,000 + 40,000,000 + 5,000,000 + 600,000 + 20 + 3
1. Write the missing numbers or words.
a) In 3,057,412, the digit is in the millions place.
b) In 82,606,197, the digit 0 is in the place and its value is .
c) In 519,208,464, the digit is in the hundred millions place and its value is .
2. Write the missing numbers.
a) 4,681,005 = 4,000,000 + + 80,000 + 1,000 + 5
b)
c) 760,148,352 = + 148,000 + 300 + 52
d) 49,507,261 = 49 millions thousands 26 tens 1 one
e) 2,900 thousands 16 tens =
f) 800 millions 90 tens 3 ones =
3. What is the value of the digit 2 in each of the following numbers?
a) 4,634,210 b) 32,143,510
c) 206,199,001
d) 55,382,148
Exercise 1.3 Comparing and ordering numbers
Coursebook Recap
Compare the digits from left to right. 45,306,230 has the most number of digits. So, it is the greatest. The other two numbers have the same digits up to the hundreds place. Compare their tens digits: 0 < 2. So, 4,530,602 < 4,530,623.
Arranging them in order, beginning with the greatest, we get: 45,306,230, 4,530,623, 4,530,602 (greatest)
1. Write > or <. a) 9,876,543 10,001,109 b) 308,417,365 308,074,563
2. Arrange the numbers in order. Begin with the least.
a) 3,508,196, 3,506,597, 3,506,975 b) 83,705,219, 907,352,108, 83,750,291
< > 3,506,597, 3,506,975, 3,508,196 83,705,219, 83,750,291, 907,352,108
2. Arrange the numbers in order. Begin with the greatest. a) 479,911,585, 79,911,588, 473,911,588 b) 6,482,915, 64,281,509, 6,428,951
479,911,585, 473,911,588, 79,911,588 64,281,509, 6,482,915, 6,428,951
Exercise 1.4 Number patterns
Coursebook Recap
Complete the number pattern.
–6, –2, 2, ?, 10
4 more than 2 is 6. 4 more than 6 is 10. The missing number is 6. + 4 + 4 + 4 + 4
–6 –2 2 ? 10
The rule of the pattern is ‘Start at –6. Count forwards by fours.’.
1. Continue the number patterns.
a) Rule: Start at 40. Count backwards by tens.
40, , , , , ,
b) Rule: Start at –13. Count forwards by fours.
–13, , , , , ,
2. Complete each number pattern. Then, describe the number pattern.
a) –9, –7, –5, , –1, 1,
Rule:
Start at –9. Count forwards by twos.
b) 4, 1, , –5, –8, , –14
Rule:
c) 17, 12, , 2, –3, , –13
Rule:
Start at 4. Count backwards by threes.
d) –24, , –4, 6 , 26, 36
Rule:
Start at –24. Count forwards by tens.
Rule:
Start at 17. Count backwards by fives.
e) , –32, –29, , –23, , –17
Start at –35. Count forwards by threes. –2 –14 7
Unit 2 Rounding Numbers
Exercise 2.1 Rounding whole numbers
Coursebook Recap
Round 6,374,092 to the nearest hundred thousand.
6,300,000 6,400,000 6,374,092
The digit to the right of the hundred thousands place is greater than 5. So, we round up.
6,374,092 is between 6,300,000 and 6,400,000. It is nearer to 6,400,000 than to 6,300,000. So, we round up.
6,374,092 is 6,400,000 when rounded to the nearest hundred thousand.
6,374,092 ≈ 6,400,000
1. Round each number to the nearest ten.
a) 4,367 ≈
b) 58,912 ≈
c) 703,485 ≈ d) 9,246,731 ≈
e) 125,679 ≈ f) 8,004,263 ≈
2. Round each number to the nearest hundred.
a) 3,482 ≈ b) 67,951 ≈
c) 804,276 ≈ d) 5,319,842 ≈
e) 249,650 ≈ f) 7,003,518 ≈
3. Round each number to the nearest thousand.
a) 6,284 ≈ b) 92,516 ≈
c) 705,432 ≈ d) 4,672,891 ≈
e) 318,750 ≈ f) 9,010,249 ≈
4,370 58,910 703,490 125,680 8,004,260 9,246,730 3,500 68,000 804,300 5,319,800 249,700 7,003,500 6,000 93,000 705,000 4,673,000 319,000 9,010,000
4. Round each number to the nearest ten thousand.
a) 251,312 ≈ b) 437,543 ≈
c) 8,054,631 ≈ d) 6,278,914 ≈
e) 5,725,097 ≈ f) 1,000,986 ≈
5. Round each number to the nearest hundred thousand.
a) 541,321 ≈ b) 850,987 ≈
c) 6,304,092 ≈ d) 1,867,234 ≈
e) 4,214,361 ≈ f) 13,954,364 ≈
6. Round each number to the nearest million.
a) 2,532,070 ≈ b) 1,964,376 ≈
c) 4,603,986 ≈ d) 5,407,092 ≈
e) 6,093,179 ≈ f) 29,804,387 ≈
7. Round 54,572,189 to the nearest a) thousand. b) ten thousand. c) hundred thousand. d) million.
3,000,000 2,000,000 5,000,000 5,000,000 6,000,000 30,000,000 54,572,000 54,570,000 54,600,000 55,000,000 250,000 8,050,000 5,730,000 500,000 900,000 6,300,000 1,900,000 4,200,000 14,000,000 440,000 6,280,000 1,000,000
Chapter 1: Practice 2.1
Unit 3 Factors, Square Numbers and Cube Numbers
Exercise 3.1 Finding factors of a whole number
Coursebook Recap
Find all the factors of 125.
1 × 125 = 125
5 × 25 = 125
The factor pairs of 125 are (1, 125) and (5, 25). The factors of 125 are 1, 5, 25 and 125.
1. Write the missing factors.
a) 4 × = 76 b) 88 = 8 × c) 15 × = 105 d) 135 = 9 ×
2. Find all the factor pairs of 120. Then, list its factors.
19 7 (1, 120), (2, 60), (3, 40), (4, 30), (5, 24), (6, 20), (8, 15), (10, 12)
3. List all the factors of:
a) 85: . b) 144:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 1, 5, 17, 85
The factors of 120 are .
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 15 11
4. Which of the following numbers has 12 as a factor?
76, 96, 110, 125
Exercise 3.2 Identifying square numbers
Coursebook Recap
When we multiply a number by itself, we get the square of the number. The square of a whole number is called a square number.
5 × 5 = 25
52 = 25 We read 52 as 5 squared.
The square of 5 is 25. 25 is a square number.
1. Draw a diagram to show that 16 is a square number.
2. Complete the multiplication sentences, then write the square numbers. a)
4. Circle the square numbers.
5. Write all the square numbers that are between 40 and 140.
64,
Exercise 3.3 Identifying cube numbers
Coursebook Recap
When we multiply a number by itself two times, we get the cube of the number. The cube of a whole number is called a cube number.
3 × 3 × 3 = 27 33 = 27 We read 33 as 3 cubed. The cube of 3 is 27. 27 is a cube number.
1. Draw a diagram to show that 8 is a cube number.
2. Complete the multiplication sentences, then write the cube numbers.
a) 23 = × × = b) 53 = × × =
3. Circle the cube numbers.
4. Write all the cube numbers that are between 20 and 130.
27, 64, 125 8 and 64
5. Write two cube numbers between 1 and 125 that are also even numbers.