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1.04 Estimation and reasonable answers

Worksheet
Estimations
1

For each of the following expressions:

i

Round both numbers to the nearest 10.

ii

Calculate the estimate.

a

99 + 61

b

63 - 22

c

28 \times 31

d

447 \times 21

2

For each of the following expressions:

i

Round the numbers to the nearest 100, where appropriate.

ii

Calculate the estimate.

a

898 - 132

b

765 + 171

c

347 \times 5

3

For each of the following expressions:

i

Round both numbers to the nearest 1000.

ii

Calculate the estimate.

a

7452 + 4193

b

9848 - 3469

4

Estimate the value of the following:

a

2692 + 3669

b

3620 - 1082

c

6534 + 7418 + 1240

d

446 \times 54

e

448 \times 39

f

8163 \div 23

g

4127 \div 19

h

5523 + 321 + 59

5

Which of the following is closest to the sum 33 + 42 + 24?

A
10
B
100
C
1000
6

Consider the sum 947 + 826 + 12.

a

Estimate the answer if each number is rounded to the nearest ten.

b

Estimate the answer if each number is rounded to the nearest hundred.

c

Find the exact value of the sum.

d

Which answer is the most accurate, part (a) or part (b)?

7

Consider the sum 24.6 + 718.94.

a

Estimate the sum by rounding each number to the nearest ten.

b

Estimate the sum by rounding each number to the nearest hundred.

c

Find the exact value of the sum.

d

Which estimate is the most accurate, part (a) or part (b)?

8

For each of the following multiplication problems:

i

Estimate the answer to the multiplication.

ii

Check your estimate in part (a) is close, by calculating the actual product, rounded to the nearest tenth.

a
9.82 \times 12.98
b
19.66 \times 7.12
c
94.12 \times 0.97
d
2.93 \times 995
9

For each of the following division problems:

i

Estimate the answer to the division.

ii

Check your estimate in part (a) is close, by calculating the actual division, rounded to the nearest tenth.

a
26.99 \div 8.98
b
41.72 \div 2.86
c
54.12 \div 0.89
d
182.33 \div 5.98
Checking reasonableness
10

Are the following calculations correct?

a

57 - 28 = 31

b

7928 + 14 = 7942

c

9352 + 47 = 479\,352

d

4192 + 5968 = 9160

e

9533 - 5933 = 4400

f

189\,672 ÷ 14 = 189\,672 ÷ 2 ÷ 7

11

Are the following statements reasonable?

a

59 - 27 is approximately equal to 30.

b

68 - 27 is approximately equal to 60.

c

2883 - 2831 is approximately equal to 80 - 30.

d

6871 - 5832 is approximately equal to 70 - 30.

e

67 - 29 is approximately equal to 40.

f

4 \times 88 will be less than 320.

g

4 \times 83 will be greater than 320.

h

3024 \times 5 = 151\,020

i

9352 \times 4761 will be greater than 36\,000\,000.

12

Suppose we want to check the subtraction problem 82 - 80 = 2.

a

Which two numbers must we add?

b

What should the two numbers add up to?

13

State whether the following products are close to 1819:

a

98 \times 97

b

201 \times 9

c

33 \times 59

d

33 \times 18

14

Is the following division close to 200?

624 \div 3

15

State whether the following is true or false:

a

Dividing by 6 is the same as dividing by 3 and then dividing by 3 again.

b

4000 is a reasonable estimate for 42 \times 8.

c

400 is a reasonable estimate for 2002 \div 5.

d

If apples cost \$3.25/\text{kg}, then 3.5\text{ kg} of apples will cost about \$9.25.

e

If oranges cost \$2.25/\text{kg}, then 5\text{ kg} of oranges will cost about \$11.

Applications
16

Weatley Coach Lines buses will carry on average 33 passengers per trip. Each day, the company sends out 78 buses and each bus completes on average 23 trips per day.

Estimate the number of people that travel on the buses each day.

17

Fiona started a savings account with the aim of reaching \$272\,088. If, on average, Fiona deposits \$5200 every month, estimate the number of months it will take to reach her goal.

18

Ursula collects beetles. She knows that she has exactly 169 of them. Ursula has to move house this week, and must buy storage boxes to transport them.

Will 9 boxes that hold 20 beetles each be enough storage?

19

Brad and Bill went out one evening. Bill said:

"I have \$18.40, which is about \$20. This food stall charges \$9.50 for a kebab, which is about \$10. That means I have enough money to pay for both of us to get a kebab."

a

Is Bill being reasonable? Explain your answer.

b

Brad says, "I can put \$5 towards our meal, then we can both afford a kebab." Is Brad correct? Explain your answer.

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Outcomes

F.3

ascertain the reasonableness of answers to arithmetic calculations

F.4

use leading-digit approximation to obtain estimates of calculations

F.6

check results of calculations for accuracy

F.10

apply approximation strategies for calculations

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