Solved Worksheet on Estimating Quotients

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Diego Tue, Jan 25, 2022 12:21 PM UTC

Estimating Quotients. To estimate the quotient, we first round off the divisor and the dividend to the nearest tens, hundreds, or thousands and then divide the rounded numbers. In a division sum, when the divisor is made up of 2 digits or more than 2 digits, it helps if we first estimate the quotient and then try to find the actual number.

1. 10-NEM6 WBAns 8/8/05 3:10 PM Page 88
CHAPTER 10
1 Estimating Quotients
Goal Estimate quotients when dividing decimal numbers.
1. Estimate each quotient. Show your work. At-Home Help
a) 8.4 ÷ 5 To estimate a quotient when dividing
a decimal number by a one-digit
Suggested answer: Round 8.4 to 8.0. number, use one of these methods.
Rename 8 ones as 80 tenths. • Round the decimal number to the
80 tenths ÷ 5 = 16 tenths nearest whole number.
8.4 ÷ 5 is about 1.6. For example: 5.9 3
Round 5.9 to 6.
b) 13.7 ÷ 7 632
Suggested answer: Round 13.7 to 14. 5.9 3 is about 2.
14 ÷ 7 = 2 • Rename the decimal number.
13.7 ÷ 7 is about 2.
For example: 2.8 3
2.8 is close to 2.7, which is an
c) 18.3 ÷ 4 easier number to divide by 3.
Suggested answer: 4 x = 18.3 Rename 2.7 as 27 tenths.
27 tenths 3 9 tenths, or 0.9
4 x 4.0 = 16.0
2.8 3 is about 0.9.
4 x 5.0 = 20.0
4 x 4.5 = 18.0 • Rewrite the division as a
multiplication question.
18.3 ÷ 4 is about 4.5.
For example: 7.7 6
d) 24.2 ÷ 3 6 7.7
Suggested answer: Round 24.2 to 24. 6 1.0 6.0
6 1.1 6.6
24 ÷ 3 = 8
6 1.5 9.0
24.2 ÷ 3 is about 8.
7.7 6 is between 1.1 and 1.5,
or about 1.3.
2. Ray bought 15.5 m of wire to make four sculptures
with equal lengths of wire. Estimate the length of
wire for each sculpture.
Suggested answer:
The problem can be solved by calculating 15.5 m ÷ 4.
4 x = 15.5
4 x 3.0 = 12.0
4 x 4.0 = 16.0
4 x 3.5 = 14.0
The answer is between 3.5 and 4.0.
15.5 m ÷ 4 is about 3.75.
Ray needs about 3.75 m of wire for each sculpture.
88 Answers Chapter 10: Dividing Decimals Copyright © 2006 Nelson

2. 10-NEM6 WBAns 8/8/05 3:10 PM Page 89
CHAPTER 10
2 Dividing Money
Goal Solve problems by dividing money.
You will need a calculator. At-Home Help
1. Use a calculator to divide. Use multiplication To solve division problems involving
money, use multiplication or
to check your answers. 2 estimation to check your answers.
a) $27.84 3 $9.28 $ 9 .2 8
For example: Four friends share the
x 3 cost of three DVDs equally. The DVDs
$ 2 7 .8 4 cost $26.99, $22.99, and $16.99.
What is the cost for each person?
1 3
$7.37 $ 7 .3 7 (total cost)
b) $36.85 5 $26.99 $22.99 $16.99 $66.97
x 5
$ 3 6. 8 5 $66.97 4 $16.74
Check by multiplying:
1 1
c) $29.50 2 $14.75 $ 1 4 .7 5 22 1
x 2 $16.74
4
$ 2 9 .5 0 $66.96
3 3 Check by estimating:
d) $45.96 6 $7.66 $ 7 .6 6 Estimated total cost:
x 6 $27 $23 $17 $67
$ 4 5 .9 6 Estimated cost per person:
67 4 is close to 68 4 17,
2 5
or about $17
e) $51.66 7 $7.38 $ 7 .3 8
x 7
$ 5 1 .6 6
2. Lara and two friends bought a book for $28.95, a CD for $22.99, and
a DVD for $26.85. Each person paid the same amount.
a) What was the cost for each person? Use a calculator.
Suggested answer: (total cost) $ 2 8 .9 5
2 2 .9 9
+ 2 6 .8 5
$ 7 8 .7 9 $78.79 ÷ 3 = $26.26
b) Use estimation to show that your answer is reasonable.
Suggested answer: Estimated total cost: 30 + 23 + 27 = 80
Estimated cost per person: 80 ÷ 3 is close to 81 ÷ 3 = 27
My estimate of $27 is close to $26.26. So my answer is reasonable.
Copyright © 2006 Nelson Answers Chapter 10: Dividing Decimals 89

3. 10-NEM6 WBAns 8/8/05 3:10 PM Page 90
CHAPTER 10
3 Dividing Decimals by One-Digit Numbers
Goal Express quotients as decimal numbers to tenths.
1. Divide. Check two answers using multiplication. At-Home Help
a) 23.4 3 d) 6 37
.2
To divide a decimal tenth by
a whole number, use the same
7 .8 6 .2
procedure as dividing two
3 23.4
6 3
7 .2 whole numbers.
21 36
For example:
2 .4 1 .2
2 .4 1 .2 8 .5
0 0 9 7
65
.
72 9 8 72
4 .5
b) 30.4 4 e) 44.5 ÷ 5
4 .5 9 0.5 4.5
7 .6 8 .9 0
4 30.4
5 4
4 .5
4 To check if a quotient is reasonable,
28 40
use multiplication or estimation.
2 .4 4 .5 8 .9
2 .4 4 .5 x 5 For example:
0 0 4 4 .5 4
8.5
9
c) 7 41.3
f) 8 25
.6
76.5
5 .9 3 .2
Estimate:
7 41.3
8 2
5 .6 8 10 80 or 80 10 8
35 6 24
6 .3 5 .9 1 .6
6 .3 x 7 1 .6
0 4 1 .3 0
2. Sheila has 3.0 kg of raisins. She keeps one-half for herself. She divides the
remaining amount equally among three friends. How many kilograms of raisins
does each person get? Show your work.
Suggested answer:
(Sheila) 3.0 kg ÷ 2 = 1.5 kg
(each friend) 1.5 kg ÷ 3 = 0.5 kg
0 .5
3 1.5

1 .5
0 .0
90 Answers Chapter 10: Dividing Decimals Copyright © 2006 Nelson

4. 10-NEM6 WBAns 8/8/05 3:10 PM Page 91
CHAPTER 10
4 Dividing by 10, 100, 1000, and 10 000
Goal Divide whole and decimal numbers by 10, 100, 1000, and 10 000
using mental math.
1. Calculate. Use mental math. At-Home Help
a) 321 100 3.21 To divide a decimal tenth by 10, 100,
or 1000, move the digits to the right
b) 25 10 2.5 one, two, or three places.
0.45 For example,
c) 4.5 10
553 10 55.3
d) 321 10 000 0.0321
553 100 5.53
e) 18 1000 0.018 553 1000 0.553
0.607 553 10 000 0.0553
f ) 60.7 100
55.3 10 5.53
g) 58 240 1000 58.24
55.3 100 0.553
h) 58 240 10 000 5.824 55.3 1000 0.0553
55.3 10 000 0.005 33
2. Chris has 12.3 L of juice. He wants to pour equal amounts of juice
into 10 glasses. How many litres of juice will be in each glass?
Suggested answer:
12.3 L ÷ 10 = 1.23 L
3. 56.2 kg of rice is divided equally into 100 containers. How many kilograms
of rice are in each container?
Suggested answer:
56.2 kg ÷ 100 = 0.562 kg
4. Concert organizers ordered 3550 L of water for an audience of 10 000 people.
How many milliltres of water will be available for each person?
Suggested answer:
3550 L ÷ 10 000 = 0.355 L
0.355 x 1000 = 355 mL
Copyright © 2006 Nelson Answers Chapter 10: Dividing Decimals 91

5. 10-NEM6 WBAns 8/8/05 3:10 PM Page 92
CHAPTER 10
5 Solving Problems by Working Backward
Goal Use a working-backward strategy to solve problems.
Lynne has 17.2 m of ribbon to wrap two sizes of gifts. At-Home Help
There are four small gifts and one larger gift. She needs Some problems can be solved
4.8 m to wrap the larger gift. How much ribbon does she by working backward.
need to wrap each smaller gift? Use the problem-solving steps
Understand the Problem, Make
Suggested answer:
a Plan, Carry Out the Plan, and
Understand the Problem Look Back.
I need to determine the length of ribbon for each of the
smaller gifts. I know the total length of ribbon and the length
needed for the larger gift.
Make a Plan
I’ll draw a diagram to represent the problem.
17.2 m
? ? ? ? 4.8 m
The diagram shows four lengths of ribbon added to the length of 4.8 m. The total length is 17.2 m.
I can work backward to estimate and calculate the length needed for each of the four small gifts.
Carry Out the Plan
I estimate the length needed for each small gift is greater than 3 m.
Step 1: I subtract the length used for the larger gift from the total length. The length needed
for all four smaller gifts is 12.4 m.
Step 2: I divide the length needed for the four gifts to determine the length for each gift.
12.4 m ÷ 4 = 3.1 m
The length needed for each of the smaller gifts is 3.1 m.
92 Answers Chapter 10: Dividing Decimals Copyright © 2006 Nelson

6. 10-NEM6 WBAns 8/8/05 3:10 PM Page 93
CHAPTER 10
Test Yourself
Circle the correct answer.
1. Which quotient is the closest estimate for 14.6 3?
A. 4 B. 5 C. 6 D. 7
2. Miranda got 4.94 when she divided 34.58 by 7. Which method is incorrect to use
to check her answer?
A. Multiply 34.58 by 4.94. C. Round 4.94 to 5. Then multiply by 7.
B. Multiply 4.94 by 7. D. Use a calculator to divide 34.58 by 7.
3. Which quotient answers the question $46.32 4?
A. $11.58 B. $11.98 C. $12.58 D. $12.98
4. Royce and four friends bought a CD and a DVD. The CD cost $16.99 and the DVD
cost $24.96. Each person paid the same amount. What was the cost for each person?
A. $11.39 B. $10.75 C. $10.48 D. $8.39
5. Yvette paid $26.08 for eight different flags. Each flag cost the same amount.
How much did each flag cost?
A. $2.61 B. $3.00 C. $3.26 D. $3.50
6. What is the quotient of 67.2 3?
A. 21.8 B. 22.4 C. 24.3 D. 25.4
7. Nigel bought 4.5 kg of trail mix. He kept 2 kg for himself. He divided the remaining
amount equally among five friends. How many kilograms of trail mix did each friend get?
A. 0.3 kg B. 0.4 kg C. 0.5 kg D. 0.6 kg
8. Which quotient is incorrect?
A. 40.3 10 4.03 C. 3.5 100 0.35
B. 690 1000 0.69 D. 7 1000 0.007
9. 20.4 L of fruit punch is divided equally into 100 containers. How many litres
of punch are in each container?
A. 204 L B. 2.04 L C. 0.204 L D. 0.024 L
10. Nemil added 0.6 years to his age, and divided that result by 4. The final answer
was 2.4. How old is Nemil?
A. 8 B. 9 C. 10 D. 11
Copyright © 2006 Nelson Answers Chapter 10: Dividing Decimals 93

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