Detailed Explanation of Estimating Products

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In this pdf, we will be estimating products. In order to estimate products, we round the given factors to the required place value. Estimating products help us to check the reasonableness of an answer. To estimate the product, we first round off the multiplier and the multiplicand to the nearest tens, hundreds, or thousands and then multiply the rounded numbers.

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CHAPTER 9
1 Estimating Products
Estimate products of decimal tenths and money amounts using a
Goal variety of strategies.
1. Estimate each product. Show your work. At-Home Help
a) 3.6 $29.55 d) 5.7 $12.77 There are several ways to estimate
the cost of an item.
Suggested answer: Suggested answer:
4 x $30 = $120 or 6 x $12 = $72 or For example, to estimate the cost
2 3 of 1.3 kg of salmon that costs
3 x $30 plus of $30 5 x $12 plus of $12 $17.61 per kilogram, use one of
3 4
= $90 + $20 = $60 + $9 these methods.
= $110 = $69 1 $20 $20 or
b) 2.4 $16.59 e) 6.6 $24.41 1
1 $18 plus of $18
3
Suggested answer: Suggested answer: $18 $6
$24
3 x $16 = $48 or 7 x $25 = $175 or
1 2
2 x $16 plus of $16 6 x $24 plus of $24 Use rounding or numbers that are
2 3 easier to work with.
= $32 + $8 = $144 + $16
= $40 = $160
c) 4.3 $18.86 f) 8.4 $49.48
Suggested answer: Suggested answer:
4 x $20 = $80 or 8 x $50 = $400 or
1 1
4 x $18 plus of $18 8 x $50 plus of $50
3 2
= $72 + $6 = $400 + $25
= $78 = $425
2. Estimate each cost. Use a method that will give the answer closest to the actual cost.
a) 1.2 kg at $16.88 per kilogram d) 4.3 kg at $29.10 per kilogram
Suggested answer: Suggested answer:
1
1 x $17 = $17 4 x $30 plus of $30
3
= $120 + $10
= $130
b) 0.6 kg at $21.77 per kilogram e) 5.4 kg at $31.74 per kilogram
Suggested answer: Suggested answer:
2 1
of $21 = $14 5 x $32 plus of $32
3 2
= $160 + $16
= $176
c) 1.8 kg at $18.45 per kilogram f) 8.7 kg at $39.25 per kilogram
Suggested answer: Suggested answer:
3
2 x $18 = $36 8 x $40 plus of $40
4
= $320 + $30
= $350
Copyright © 2006 Nelson Answers Chapter 9: Multiplying Decimals 79

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CHAPTER 9
2 Multiplying by 1000 and 10 000
Goal Multiply decimal tenths, hundredths, and thousandths by 1000 and 10 000.
1. Calculate. At-Home Help
a) 1000 0.501 501 To multiply a decimal tenth,
hundredth, or thousandth by 1000,
b) 14.82 1000 14 820 move all digits to the left three places.
To multiply by 10 000, move all
c) 10 000 29.086 290 860 digits to the left four places. You
58 000 can see the pattern by multiplying
d) 5.8 10 000 by 10, 100, 1000, or 10 000.
e) 1000 67.3 67 300 For example,
29.8 10 298
f) 4.01 1000 4010 29.8 100 2980
29.8 1000 29 800
2. Determine the distance in metres. 29.8 10 000 298 000
a) 51.42 km 51 420 m
b) 0.986 km 986 m
c) 8.023 km 8023 m
d) 18.7 km 18 700 m
e) 30.002 km 30 002 m
f) 84.06 km 84 060 m
3. Jamie rides 4.26 km on his bicycle each day.
About how far does he ride in 3 years?
Suggested answer:
One year has about 300 days.
So 3 years have about 1000 days.
I estimate 4.26 km x 1000 = 4260 km.
4. Dana walks about 0.76 m in each step. How far could she travel if she takes
10 000 steps?
0.76 m x 10 000 = 7600 m
80 Answers Chapter 9: Multiplying Decimals Copyright © 2006 Nelson

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CHAPTER 9
3 Multiplying Tenths by Whole Numbers
Multiply decimal tenths by whole numbers using models, drawings,
Goal and symbols.
1. Multiply. Show your work. At-Home Help
a) 14.3 5 c) 20.7 3 To multiply a decimal tenth by
a whole number, you can use
21 2 regrouping or partial products.
1 4. 3 2 0 .7 For example:
x 5 x 3
2 2
7 1. 5 6 2 .1
3 5 .6
4
b) 2.8 6 d) 82.4 9 1 4 2 .4
Suggested answer: Suggested answer: or
4 23
2 2
2 8 tenths 8 2 4 tenths 3 5 6 tenths
x 6 x 9 4
168 tenths 7 4 1 6 tenths 1 4 2 4 tenths
= 16.8 = 741.6 1 4 2.4
2. A fruit pie uses 1.3 kg of peaches, 50.5 g of ground almonds, and 2 packages
of ricotta. Serina needs to make 4 pies for a family gathering.
a) How much of each ingredient is needed?
Suggested answer:
peaches almonds ricotta
1 2
1 . 3 kg 5 0 . 5 g 2 packages
x 4 x 4 x 4
5 . 2 kg 2 0 2 . 0 g 8 packages
b) One kilogram of peaches costs $6. What is the total cost of the peaches needed?
Suggested answer:
1
5. 2
x 6
31.2
The total cost of the peaches is $31.20.
Copyright © 2006 Nelson Answers Chapter 9: Multiplying Decimals 81

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CHAPTER 9
4 Multiplying by 0.1, 0.01, or 0.001
Goal Multiply by 0.1, 0.01, or 0.001 using mental math.
1. Multiply. At-Home Help
a) 245 0.01 2.45 To multiply a whole number by 0.1,
0.01, or 0.001, move the digits to
the right.
b) 312 0.1 31.2
For example,
298 10 000 2 980 000
c) 405 0.001 0.405 298 1000 298 000
298 100 29 800
298 10 2980
d) 67 0.01 0.67 298 1 298
298 0.1 29.8
298 0.01 2.98
e) 89 0.001 0.089
298 0.001 0.298
f) 42 0.1 4.2
g) 540 0.01 5.4
h) 30 0.001 0.03
2. Determine the missing measurement.
a) 45 g 0.045 kg d) 202 m 0.202 km
b) 57 mm 5.7 cm e) 368 g 0.368 kg
c) 62 cm 0.62 m f) 250 mm 25 cm
3. What is each measurement?
a) a line of 804 cubes, each 0.01 m long, c) a 480 g bag of sunflower seeds,
in metres in kilograms
8.04 m 0.48 kg
b) a line of 62 boxes, each 0.1 m wide, d) a 22 g candy, in kilograms
in metres 0.022 kg
6.2 m
82 Answers Chapter 9: Multiplying Decimals Copyright © 2006 Nelson

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CHAPTER 9
5 Multiplying Multiples of Ten by Tenths
Goal Multiply to calculate the decimal portion of a multiple of 10.
1. Calculate. Show your work. At-Home Help
a) 0.3 250 75 d) 0.6 800 480 To multiply a decimal tenth by a
whole number, you can write the
Suggested answer: Suggested answer:
decimal tenth as a multiple of 10.
0.1 x 250 = 25 0.1 x 800 = 80
3 x 25 = 75 6 x 80 = 480 For example, 0.4 0.1 4
To multiply 0.4 320, multiply
b) 0.1 850 85 e) 0.5 640 320 0.1 320 32.
Then multiply 4 32 128.
85 Suggested answer:
0.4 320 128
0.1 x 640 = 64
5 x 64 = 320
c) 0.4 530 212 f) 0.8 2650 2120
Suggested answer: Suggested answer:
0.1 x 530 = 53 0.1 x 2650 = 265
4 x 53 = 212 8 x 265 = 2120
2. At Neil’s family picnic, 10 people ate 0.6 of 6400 g of roast chicken and 0.5 of
a 4500 mL container of potato salad.
a) How much roast chicken did Neil’s family eat?
Suggested answer: 0.1 x 6400 g = 640 g
6 x 640 g = 3840 g
b) How much potato salad did Neil’s family eat?
Suggested answer: 0.1 x 4500 mL = 450 mL
5 x 450 mL = 2250 mL
c) Each person ate the same amount of potato salad. How much potato salad
did each person eat?
Suggested answer: 2250 mL ÷ 10 = 225 mL
3. Students from two schools worked at a food bank. One school had 450 students.
The other school had 360 students. Eight-tenths of the students in each school
participated. How many more students participated from the school of 450 than
the school of 360? Suggested answer:
(school of 450) 0.1 x 450 = 45 (school of 360) 0.1 x 360 = 36
8 x 45 = 360 8 x 36 = 288
difference = 360 – 288
= 72 students
Copyright © 2006 Nelson Answers Chapter 9: Multiplying Decimals 83

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CHAPTER 9
6 Communicate About Problem Solving
Goal Explain how to solve problems involving decimal multiplication.
1. Janice exercises for 360 min each week. At-Home Help
She walks for 0.6 of the time, and rides When writing a solution to a problem,
her bicycle for the rest of the time. use the problem-solving model.
• Understand the Problem
a) For how many minutes does Janice walk? • Make a Plan
Suggested answer: • Carry Out the Plan
• Look Back
Understand the Problem
I need to find out how many minutes Janice spends Make sure you communicate
your thinking clearly. Use the
walking.
Communication Checklist.
Make a Plan
6
I will model 0.6 using a rectangle. 0.6 is the same as . Communication Checklist
10 ✓ Did you model the problem-
So I divide the rectangle into 10 equal parts and
solving process?
shade 6 of them. ✓ Did you show all your steps?
360 min ✓ Did you use a model or diagram?
✓ Did you explain your thinking?
✓ Did you state your solution clearly?
I will determine how many minutes are represented by
each part. Then I will multiply that number by 6, because 6 parts are shaded.
Carry Out the Plan
Since 360 is divided into 10 parts, each part represents 360 ÷ 10 = 36 min.
6 x 36 min = 216 min
Janice walks for 216 min each week.
b) For how many minutes does Janice ride her bicycle?
Suggested answer:
Understand the Problem
I need to find how many minutes Janice rides her bicycle.
Make a Plan
I know that the total time Janice exercises is 360 min. Since she walks for 216 min, the rest
of the time she rides her bicycle. So I need to subtract.
Carry Out the Plan
360 min – 216 min = 144 min
Janice rides her bicycle for 144 min.
84 Answers Chapter 9: Multiplying Decimals Copyright © 2006 Nelson

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CHAPTER 9
7 Choosing a Multiplication Method
Goal Justify the choice of a multiplication method.
1. Multiply. Did you use mental math, pencil and At-Home Help
paper, or a calculator? If numbers are simple to multiply,
you can use mental math. Multiplying
a) 0.6 5 e) 2.9 4
by 0.001, 0.01, 0.1, 10, 100, and
3 Suggested answer: 1000 can be done mentally.
mental math 2x4=8
For example, 5.7 100 570.
0.9 x 4 = 3.6
8 + 3.6 = 11.6 If you can multiply numbers without
a lot of partial products, use pencil
pencil and paper
and paper.
b) 1.8 9 f) 5.7 100
For example, 8.2 6 49.2.
7 570
1 .8 mental math If you have to use a lot of partial
x 9 products, use a calculator.
1 6 .2 For example,
pencil and paper 79.523 91 7236.593.
c) 0.52 4 g) 0.04 100
0 .5 2 4
x 4 mental math
2 .0 8
pencil and paper
d) 0.37 100 h) 0.8 7
37 5.6
mental math mental math
2. Explain why you chose the method you did for three parts in Question 1.
Suggested answer:
Part a): I used mental math because I know that 6 x 5 = 30. So 0.6 x 5 = 3.
Part b): I used pencil and paper because the numbers were too hard to multiply in my head.
Part e): I used pencil and paper because I had to keep track of the partial products. Then I
added the partial products in my head.
Copyright © 2006 Nelson Answers Chapter 9: Multiplying Decimals 85

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CHAPTER 9
Test Yourself Page 1
Circle the correct answer.
1. Which estimate would be closest to the actual product? 8.3 21.20
1
A. 8 21 C. 8 21 plus of 21
3
1
B. 9 22 D. 9 24 plus of 24
3
2. Which is the best estimate for 0.8 kg at $28.95 per kilogram?
A. $16 B. $18 C. $29 D. $32
3. What is the product of 1000 and 25.064?
A. 250.64 B. 2506.4 C. 25 064 D. 250 640
4. What is the product of 0.891 and 1000?
A. 8.91 B. 89.1 C. 891 D. 8910
5. What is 5.007 km in metres?
A. 50 007 m B. 50.07 m C. 500.7 m D. 5007 m
6. What is the product of 6.2 and 7?
A. 42.2 B. 43.4 C. 44.4 D. 42.9
7. What is the product of 503 and 0.01?
A. 0.503 B. 5.03 C. 50.3 D. 503
8. What is the product of 0.1 and 827?
A. 8270 B. 827 C. 8.27 D. 82.7
9. One muffin has a mass of 0.025 kg. What is the mass in grams?
A. 250 g B. 0.25 g C. 2.5 g D. 25 g
10. What is the product of 0.4 and 3260?
A. 652 B. 978 C. 1304 D. 1448
86 Answers Chapter 9: Multiplying Decimals Copyright © 2006 Nelson

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CHAPTER 9
Test Yourself Page 2
11. A library has 5460 books. Three-tenths of the books are mysteries. How many
mystery books are there?
A. 546 books B. 1638 books C. 1820 books D. 2730 books
12. Jason wants to multiply 0.6 by 920. He wrote
0.1 920
92
What are the missing numbers?
A. 92, 6, 552 B. 9.2, 6, 55.2 C. 92, 60, 5520 D. 92, 60, 552
13. Lina saved $240 planting trees. She spent 0.4 of that amount on a new jacket. How
much did she spend on the jacket?
A. $60 B. $96 C. $120 D. $9.60
14. Which product is greatest?
A. 1000 0.6 B. 1000 0.105 C. 1000 0.92 D. 1000 0.033
15. Mitch bought 0.6 kg of grapes.
$ 3.00
One kilogram cost $3.00 on sale.
The regular price was $4.00 per kilogram.
How much did Mitch save?
A. $1.80 C. $2.40
B. $0.80 D. $0.60
Copyright © 2006 Nelson Answers Chapter 9: Multiplying Decimals 87

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