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1.03 Checking reasonableness

Worksheet
Estimation
1

State whether the following sums are approximately equal to 10, 100, or 1000:

a
23 + 42 + 34
b
93 + 342 + 567
c
364 + 292 + 311
d
6 + 3 + 3
2

State whether the following sums are approximately equal to 10:

a
4 + 2 + 3
b
9 + 8 - 14
c
2 + 8 + 19
d
9 + 9 - 7
3

State whether the following sums are approximately equal to 100:

a
28 + 32 + 43
b
99 + 88 - 78
c
131 + 62 + 11
d
45 + 12 - 7
4

State whether the following sums are approximately equal to 1000:

a
452 + 213 + 334
b
99 + 188 - 68
c
948 + 827 + 18
d
946 + 28 + 14 + 19
5

Explain whether the following statements are 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.

6

Describe why the following statements are true or false.

a

4 \times 89 will be less than 320.

b

3 \times 85 will be more than 240.

7

Consider the product 37 \times 94 and determine which of the following statements are correct. Explain your choices.

A

The product is less than 4000.

B

The product is more than 2700.

C

The product is more than 4000.

D

The product is less than 2700.

8

Explain whether the following products are approximately equal to 1200:

a

33 \times 38

b
31 \times 18
c
203 \times 6
d
68 \times 69
9

Henrico says "821 \div 400 is approximately equal to 200." Describe why Henrico is correct or incorrect?

10

Jia says "4 \div 1221 is approximately equal to 300." Describe why Jia is incorrect.

11

Describe how you would approximate the following calculations to the nearest 100.

a

47 \times 93

b
178 \times 5
c
1621 \div 4
d
5513 \div 11
12

Fred says "Dividing by 6 is the same as dividing by 3 and then dividing by 3 again". Is Fred correct? Explain your answer.

13

Emma says "Multiplying by 15 is the same as multiplying by 3 and then multiplying by 5 ". Is Emma correct?

Applications
14

Michael collects padlocks. He knows that he has exactly 195 of them. Michael has to move house this week, and must buy storage boxes to transport them.

Should Michael buy 7 boxes that hold 30 padlocks each or 5 boxes that hold 30 padlocks each?

15

Ryan and Michael went out one evening. Michael said:

"I have \$17.40, which is about \$20. This restaurant charges \$9.75 for a pizza, which is about \$10. That means I have enough money to pay for both of us to get a pizza."

a

Is Michael correct? Explain your answer.

b

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

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