CHAPTE R
6
Multiply and
Divide Decimals
connectED.mcgraw-hill.com
The
BIG Idea
Investigate
How does using
estimation help me
to multiply and
divide decimals
accurately?
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r that has a digit in the
decimal decimal A numbe
ce, and beyond.
tenths place, hundredths pla
0.32
eGames
Worksheets
tenths
hundredths
Assessment
Review Vocabulary
English
compatible numbers
decimal point
rounding
238
Español
números compatibles
punto decimal
redondear
When Will I Use This?
Your Turn!
You will solve thhiis teerrr.
problem in the chap
Multiply and Divide Decimals 239
Are You Ready
for the Chapter?
Text Option
You have two options for checking
Prerequisite Skills for this chapter.
Take the Quick Check below.
Multiply.
1. 16 × 30
2. 12 × 28
3. 320 × 10
4. 34 × 21
5. 56 × 50
6. 109 × 34
7. How much will it cost for
Gary to reserve 13 lanes?
Bowling Reservations
1 lane
$12
8. Mr. Irwin bought 4 concert tickets for his family.
If each ticket costs $24, how much did Mr. Irwin spend?
Divide.
9. 114 ÷ 6
12. 1,500 ÷ 10
10. 84 ÷ 4
11. 64 ÷ 4
13. 512 ÷ 8
14. 5,000 ÷ 5
15. Hugo spent $216 on 4 sweaters. If each sweater cost
the same amount, find the cost of one sweater.
Round each decimal to the nearest whole number.
16. 2.7
17. 0.7
18. 18.2
19. 6.34
20. 9.8
21. 9.4
Online Option
240
Take the Online Readiness Quiz.
Multiply and Divide Decimals
Multi-Part
Lesson
1
PART
Multiply Decimals by Whole Numbers
A
Main Idea
I will estimate products
of whole numbers and
decimals.
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, and decimals.
GLE 0506.1.2 Apply and adapt
a variety of appropriate
strategies to problem solving,
including estimation, and
reasonableness of the solution.
B
C
Estimate Products of Whole
Numbers and Decimals
Previously, you used rounding and compatible numbers to
estimate products with whole numbers. You can use the same
methods to estimate products of whole numbers and decimals.
Use Rounding
G
GASOLINE
Mrs. James buys about 15.8 gallons of gas each
week
for her car. About how many gallons of gas does she
w
buy in 5 weeks?
Estimate the product of 15.8 and 5.
15.8 × 5
16 × 5
16 × 5 = 80
Round 15.8 to 16 because 15.8
is closer to 16 than 15.
Multiply.
So, 15.8 × 5 is about 80. Mrs. James buys about 80 gallons
of gas in 5 weeks.
SHOPPING A gel pen at a craft
store costs $1.49. Lucinda
wants to buy three gel pens,
each in a different color. She
has $6 to spend. Does Lucinda
have enough money to buy three
gel pens? Explain.
3 × $1 = $3 Estimate $1.49 as $1.
3 × $2 = $6 Estimate $1.49 as $2.
The actual cost of the pens is between $3 and $6.
Lucinda has enough money to buy three gel pens.
Lesson 1A Multiply Decimals by Whole Numbers 241
Use Compatible Numbers
Estimate the product of 19 and 11.25.
E
19 × 11.25
Compatible numbers
are numbers that are
close to the actual
numbers and easy to
multiply.
92
× 4.2
−−
−−
100
4
×−
−−
400
20 × 10 20 and 10 are compatible numbers.
20 × 10 = 200
So, 19 × 11.25 is about 200.
Use Compatible
Numbers
M
MEASUREMENT
A worker loads 16 packages onto
a truck. Each package weighs 58.5 pounds. About
how many pounds are loaded onto the truck?
Judge the reasonableness of your answer.
58.5 × 16 Estimate the product of 58.5 and 16.
60 × 20
60 and 20 are compatible numbers.
So, 58.5 × 16 is about 1,200.
The truck is holding about 1,200 pounds. Since both
numbers were rounded up, the estimate is higher than
the actual product.
Estimate each product
product. See Examples 11–44
1. 2 × $4.10
2. 5 × $12.65
3. 18.4 × 10
4. 24.7 × 3
5. A group of five friends is going to see
a movie. If one ticket costs $8.50, is
$45 a reasonable estimate for the cost
of 5 tickets? Explain.
6. About 57 people rent skates at the ice
rink each day. It costs $4.25 to rent
skates. About how much does the rink
make in skate rentals in one day?
7. A cantaloupe weighs 1.8 pounds.
About how much do 3 cantaloupes
weigh?
8.
242
Multiply and Divide Decimals
E
TALK MATH Explain how to round
18.9 to the nearest whole number.
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Begins on page EP2.
Estimate
i
each
h product.
d
See Examples 1–4
9. 4 × $4.62
13. 7.2 × 5
10. 3 × $23.07
11. $15.50 × 6
12. $16.85 × 9
14. 14.5 × 3
15. 8 × 19.7
16. 10 × 26.2
17. Measurement A turkey costs $0.89
per pound and weighs 14 pounds. Is
$15 a reasonable estimate for the cost
of the turkey? Explain.
18. A dragonfly can fly at a speed of
17.8 miles per hour. At that speed,
about how far could a dragonfly fly in
5 hours?
Art
Artsonia is the world’s largest kids’ online art museum, where
students have their own art gallery online. Friends and family can order
items like the ones shown below that display students’ artwork.
Estimate the cost of each order.
19. 4 keychains
20. 2 plush bears
21. 3 coffee mugs and 2 keychains
22. 5 mouse pads and a plush bear
23. If you have $50, how many coffee mugs can you buy?
Use the guess, check, and revise strategy.
24. OPEN ENDED Write a real-world multiplication problem involving
whole numbers and decimals in which you would use estimation
to solve. Describe the steps that you used to solve the problem.
25.
E
WRITE MATH Explain why it is important to use estimation
when solving multiplication problems involving decimals.
Lesson 1A Multiply Decimals by Whole Numbers 243
Multi-Part
Lesson
1
Multiply Decimals
PART
A
B
C
Main Idea
Multiply Decimals
by Whole Numbers
I will explore
multiplying a decimal
by a whole number.
You can use decimal models to multiply a decimal and a whole
number. Each 10 by 10 square represents 1 whole.
Materials
colored pencils
Model 0.4 × 2 using decimal models.
grid paper
0.4
Shade four rows of
each decimal model
to represent 0.4.
2
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, decimals.
Also addresses GLE 0506.1.4.
Combine both shaded
parts onto one model.
So, 0.4 × 2 = 0.8.
and Apply It
Use decimal models to solve.
1. 0.5 × 2
2. 0.2 × 3
3. 2 × 0.6
4. The product of a multiplication problem is
represented by the decimal model shown.
Write two possible factors for the model.
5.
244
E TALK MATH How could you solve
Exercises 1–3 without using decimal models?
Multiply and Divide Decimals
Multi-Part
Lesson
1
Multiply Decimals
PART
A
Main Idea
I will multiply a
decimal by a whole
number.
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, decimals.
Also addresses GLE 0506.1.7.
B
C
Multiply Decimals
by Whole Numbers
Multiplying a decimal by a whole number is similar to
multiplying whole numbers.
Find 3 × 0.96.
One Way:
Use repeated addition.
3 × 0.96 means 0.96 + 0.96 + 0.96.
21
0.96
0.96
+
0.96
−−−−
2.88
Another Way:
1
0.96
×3
−−−
2.88
Count decimal places.
There are two places to the
right of the decimal point.
Count two decimal places
from right to left in the
product.
MEASUREMENT Find the area of a
board that is 4 feet by 3.62 feet.
Estimate 4 × 3.62
2
3.62
×
−−−−4
14.48
4 × 4 or 16
There are two places to the
right of the decimal point.
Count two decimal places from right to left.
The area of the bulletin board is 14.48 square feet.
Lesson 1C Multiply Decimals by Whole Numbers
245
Multiply. See Examples 1 and 2
Multiply
1. 6 × 0.5
2. 4 × 2.6
3. 7 × 0.89
4. 3 × 2.49
5. 52 × 2.1
6. 3.4 × 7
7. A recipe for a cake calls for 3.5 cups of sugar. How many
cups of sugar are needed for 4 cakes?
8.
E
TALK MATH Is the product of 2.8 and 2 greater than 6 or
less than 6? How do you know?
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Multiply.
M
lti l See Examples
l 1 and
d2
9. 2 × 1.3
10. 3 × 0.5
11. 1.8 × 9
12. 2.4 × 8
13. 4 × 0.02
14. 0.66 × 5
15. 0.7 × 4
16. 1.59 × 7
17. 0.48 × 3
Algebra Evaluate each expression if x = 3, y = 0.2, and z = 4.5.
18. (7 × 2) × y
19. xz
20. (9 - x) × y
Use the information to solve the problem.
21. Did Sonia or Tom make more money mowing lawns? Explain.
246
Multiply and Divide Decimals
22. OPEN ENDED Write a multiplication problem in which the product
has two decimal places.
23. NUMBER SENSE Place the decimal point in the answer below to
make it correct. Explain your reasoning.
498 × 8.32 = 414336
24.
E
WRITE MATH Write a real-world problem that can be solved using
multiplication. One factor should be a decimal.
Test Practice
25. One pound off
tomatoes costss
$1.59. How
much do 5
pounds of
tomatoes
cost?
A. $5.59
C. $7.95
B. $6.59
D. $9.79
26. Mr. Thomas’ car can travel 17.6 miles
per gallon of gas. If his gas tank holds
11 gallons, how far can he travel on a
full tank of gas?
F. 176 miles
H. 286.6 miles
G. 193.6 miles
I. 352 miles
27.
SHORT RESPONSE The Marino
family bought 4 tickets to the circus.
What was the total cost of the
tickets?
ets?
28.
GRIDDED RESPONSE Vanessa
is making bracelets for a fundraiser.
Each bracelet uses 28.5 centimeters
of string. How many centimeters
of string will she need to make
20 bracelets?
Estimate each product. (Lesson 1A)
29. 2.3 × 6
30. 1.35 × 4
31. 8.7 × 17
32. Mrs. Walsh needs to buy 1.75 pounds of clay for each student
in her class. If she has 22 students, about how many pounds
of clay does she need to buy? (Lesson 1A)
Lesson 1C Multiply Decimals by Whole Numbers
247
Multi-Part
Lesson
2
PART
Multiply Decimals
A
B
C
D
Main Idea
Use Models to
Multiply Decimals
I will explore using
decimal models to
multiply decimals.
You can also use decimal models to multiply a decimal by
a decimal.
Materials
colored pencils
Find 0.3 × 0.7 using a decimal model.
Step 1
Draw a 10-by-10 decimal model.
grid paper
Each small square represents 0.01.
Get ConnectED
Step 2
Shade a rectangle that is 0.3 units wide and
0.7 units long.
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, decimals.
Also addresses GLE 0506.1.4.
0.3
0.7
There are twenty-one hundredths
in the region that are shaded.
So, 0.3 × 0.7 = 0.21.
248
Multiply and Divide Decimals
Find 0.4 × 2.4 using decimal models.
Step 1
Draw three 10-by-10 decimal models.
Step 2
Shade a rectangle that is 0.4 units wide and
2.4 units long.
0.4
2.4
Step 3
Shade the same amount of squares on a 10-by-10 grid.
There are ninety-six
hundredths in the
shaded region.
So, 0.4 × 2.4 = 0.96.
and Apply It
Use decimal models to find each product.
1. 0.4 × 0.8
2. 0.5 × 0.6
3. 0.2 × 0.9
4. 0.3 × 1.8
5. 0.6 × 2.2
6. 1.4 × 0.8
7. Diana’s house has a rectangular window on the door with a height
of 1.5 feet and a width of 0.8 feet. What is the area of the window?
8.
E
WRITE MATH How many 10-by-10 decimal models do
you need to find 0.5 × 3.2?
Lesson 2A Multiply Decimals 249
Multi-Part
Lesson
2
Multiply Decimals
PART
A
Main Idea
I will multiply a
decimal by a decimal.
Get ConnectED
B
C
D
E
Multiply Decimals
To multiply a decimal by a decimal, multiply as with whole
numbers. To decide where to place the decimal point, count the
number of decimal places in each factor. The product has the
same number of decimal places.
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, decimals.
Find 1.8 × 3.9. Estimate 1.8 × 3.9
2 × 4 or 8
1.8
×
3.9
−−−−
162
+
540
−−−−
702
one decimal place
one decimal place
7.02
Count two decimal places from the
right and place the decimal point.
So, 1.8 × 3.9 = 7.02. Check 8 ≈ 7.02 PEANUTS Nina is buying peanuts in bulk. The peanuts cost
$0.75 for each pound. She purchased 2.1 pounds of peanuts.
How much will Nina pay? Round to the nearest cent.
Find $0.75 × 2.1.
Estimate $0.75 × 2.1
0.75
×
2.1
−−−−
75
+
1500
−−−−−
1575
1.575
$1 × 2 or $2
two decimal places
one decimal place
Count three decimal places from the
right and place the decimal point.
$1.58 Round to the nearest cent.
Nina will need to pay $1.58. Check $2 ≈ $1.58 250
Multiply and Divide Decimals
Annex Zeros
GUITARS Demarcus is buying a
new guitar pick that costs $0.50.
The sales tax is found by multiplying
the cost of the guitar pick by 0.06.
What is the cost of the sales tax
for the pick?
Find 0.50 × 0.06.
0.50
×
0.06
−−−−−
300
two decimal places
two decimal places
0.0300 or 0.03 Count four decimal places from the right.
Annex zeros if needed.
The sales tax is $0.03.
Multiply. See Examples 11–33
Multiply
1. 0.6 × 0.8
2. 1.7 × 2.4
3. 0.9 × 3.8
4. 0.96 × 7.1
5. 2.6 × 3.65
6. 5.2 × 0.07
7. 0.8 × 2.78
8. 0.35 × 0.15
9. 3.24 × 6.4
10. Measurement Jocelyn’s swimming pool
is shown. Find the area of the swimming
pool.
11. A nutrition label says that one serving
out of a bag of chips has 3.7 grams of fat.
How many grams of fat are there in
2.5 servings?
12. Apples cost $0.98 per pound. How much would it cost to
purchase 5.5 pounds of apples?
13.
E
TALK MATH Compare and contrast multiplying decimals
and multiplying whole numbers.
Lesson 2B Multiply Decimals 251
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Begins on page EP2.
Multiply.
l i l See Examples 1–3
14. 0.9 × 0.3
15. 1.6 × 3.2
16. 0.5 × 6.7
17. 0.81 × 7.3
18. 5.6 × 3.9
19. 1.2 × 0.05
20. 0.28 × 0.03
21. 0.73 × 0.21
22. 5.14 × 0.4
23. 0.98 × 0.23
24. 0.11 × 0.91
25. 6.34 × 0.7
26. It costs $4.25 for one pound of roast beef. How much
will it cost to purchase 2.5 pounds of roast beef? Round
to the nearest cent.
27. A certain car travels 22.6 miles on one gallon of gasoline.
How many miles can the car travel on 3.6 gallons of gas?
Find the area of each figure.
28.
29.
1.3 m
6.4 cm
1.3 m
1.8 cm
Algebra Evaluate each expression if x = 0.3, y = 6.2, and z = 0.5.
30. xy + z
31. y × 0.4 - z
32. 3.5z + y
33. y(0.6 + 0.2)
34. yz
35. 5 - (z - x)
According to a recent U.S. Census, the population of
Virginia is about 7.07 million people.
36. About twenty-four hundredths, or 0.24, of all
the people living in the state of Virginia are
under the age of 18. How many people in
Virginia are under the age of 18?
37. If forty-nine hundredths, or 0.49, of all the people
living in Virginia are female, how many females
live in Virginia?
252
Multiply and Divide Decimals
Virginia
38. NUMBER SENSE Place the decimal point in the answer to make
it correct. Explain your reasoning. 0.7839 × 2.569 = 20138391
39. OPEN ENDED Write a multiplication problem using two decimals
that has an answer that is greater than 0.1 and less than 0.2.
40.
E
WRITE MATH Write a multiplication problem in which
the product is between 0.05 and 1.
Test Practice
41. Mikayla is buying deli meat and
cheese for sandwiches for a family
reunion. How much will she
spend on 4.5 pounds of ham
and 3.5 pounds of cheese?
43. Mr. Garner’s gas tank holds
17.5 gallons of gasoline. How much
will it cost him to fill up his gas tank
if gasoline costs $2.48 per gallon?
F. $34
G. $35
H. $42.16
I. $43.40
42.
A. $7.39
C. $20.66
B. $13.27
D. $33.93
SHORT RESPONSE To find the
amount of tax added to a purchase,
the total amount is multiplied by
0.06. If Morgan buys a pair of shoes
for $38.95, how much tax is added to
the purchase price? Round to the
nearest cent.
44.
GRIDDED RESPONSE The
average honeybee can travel
10.5 feet per second. How many
feet can the honeybee travel in
3.7 seconds?
Multiply. (Lesson 1C)
45. 12.3 × 6
46. 4.56 × 9
47. 72.3 × 22
48. A group of 9 students go rollerskating. It costs $6.75 for each
person to rollerskate. Is $54 a reasonable estimate for the cost
of 9 students to rollerskate? Explain. (Lesson 1A)
Lesson 2B Multiply Decimals 253
Multi-Part
Lesson
2
Multiply Decimals
PART
A
Main Idea
I will multiply a decimal
by powers of ten.
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, decimals.
B
C
D
E
Multiply Decimals by
Powers of Ten
Multiplying a decimal by
a power of 10 moves the
decimal point to the right
the same number of places
as the number of zeros in
the power of 10.
Decimal
Power of Ten
Product
4.26
×1
= 4.26
4.26
× 10
= 42.6
4.26
× 100
= 426
4.26
× 1,000
= 4,260
SKIMBOARD Josh will need
to make 10 payments of
$32.25 to purchase a new
skimboard. What is the total
cost of the skimboard?
Find $32.25 × 10 mentally.
$32.25 × 10 = $32.25 10 has one zero. Move the decimal one
place to the right.
= $322.50 Add a zero at the end to make fifty cents.
The total cost is $322.50.
Multiply by a Power of Ten
Greater than One
Find 0.5 × 100.
0.5 × 100 = 0.50 100 has two zeros. Move the decimal point
two places to the right. Annex zeros as needed.
= 50
Since 50 is a whole number, remove the
leading zero and decimal point.
So, 0.5 × 100 is 50.
254
Multiply and Divide Decimals
A pattern is also found when multiplying a decimal by powers
of 10 like 0.1 and 0.01 that are less than one.
Multiplying a decimal by a power of 10 that is less than one
moves the decimal point to the left the same number of places
as there are after the decimal point.
Decimal
Power of 10
Product
61.3
× 0.1
= 6.13
61.3
× 0.01
= 0.613
61.3
× 0.001
= 0.0613
Multiply by a Power of Ten
Less than One
Find 3.4 × 0.1.
3.4 × 0.1 = 3.4
x
You may need to anne
zeros to complete your
multiplication.
= 0.34
There is one place after the decimal point,
so move the decimal point in 3.4 one place
to the left.
Find 8.6 × 0.01.
8.6 × 0.01 = 08.6
= 0.086
There are two places after the decimal
point, so move the decimal point in
8.6 two places to the left.
Find each product.
product Examples 11–44
1. 0.54 × 10
2. 8.32 × 100
3. 7.46 × 1,000
4. 0.98 × 100
5. 1.63 × 10
6. 0.853 × 1,000
7. 0.72 × 0.1
8. 0.9 × 0.01
9. 67.2 × 0.001
10. 76.5 × 0.001
11. 0.81 × 0.1
12. 1.23 × 0.01
13. A music store has 10 flutes. Each flute costs $325.50.
What is the cost of all 10 flutes?
14.
E
TALK MATH Suppose you want to find the cost of
10 text messages that cost $0.25 each. Explain how you
can mentally find the cost.
Lesson 2C Multiply Decimals 255
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Find
i d each
h product.
d
Examples 1–4
15. 0.397 × 100
16. 1.76 × 100
17. 0.78 × 10
18. 0.13 × 10
19. 1.4 × 1,000
20. 4.81 × 1,000
21. 0.48 × 0.1
22. 0.93 × 0.01
23. 0.22 × 0.001
24. 1.5 × 0.01
25. 9.75 × 0.001
26. 48.5 × 0.1
27. One carton of milk costs $0.99. What is the total cost of
100 cartons of milk?
28. Measurement Mike made a model of a 300-foot building.
His model was one hundredth, or 0.01, the size of the actual building.
How tall was his model?
29. The school purchased 100 trophies to give to the honor roll students.
If one trophy costs $4.32, how much would it cost for all of the trophies?
30. Titus and Cam’s hourly charge for yard work is shown.
Suppose Titus and Cam each worked 10 hours.
How much money did they earn together?
31. The length of Jenny’s cat is 10 times
the length of her hamster. What is the
length of her cat?
Titus
Cam
$8.25/h
$5.85/h
32. What is one tenth, or 0.1, the cost of
the paintbrush?
$3
.20
The table shows a school store’s prices.
33. How much will it cost for 10 pencils and
1 notebook?
34. How much would it cost to buy 10 pens from the
school store?
256
Multiply and Divide Decimals
Item
Price
Notebook
$1.25
Pencil
$0.50
Binder
$2.15
Pen
$0.80
35. CHALLENGE Find 0.346 × 102.
36. FIND THE ERROR Rico is finding 7.5 × 100. Find and correct
his mistake.
7.5 × 100
07.5 = 0.075
37.
E
WRITE MATH Write a real-world problem that involves
multiplying a decimal by a power of 10.
Test Practice
38. Elyse is cutting strips of paper for a
scrapbook page. Each strip is
1.5 centimeters wide. How wide will
10 strips of paper be?
A. 1.5 cm
39. Neal is saving $4.25 a week for
100 weeks. How much will he have
saved altogether?
F. $4.25
G. $42.50
B. 15 cm
H. $425.00
C. 150 cm
I. $4,250.00
D. 1,500 cm
Multiply. (Lesson 2B)
40. 0.4 × 0.3
41. 0.3 × 2.8
42. 1.6 × 2.5
43. 0.26 × 2.5
44. 3.6 × 7.55
45. 4.3 × 0.04
46. Sophie and two of her friends each purchased a ticket to ride the
rollercoaster. If it costs $1.45 for 1 ticket, how much did Sophie
and her friends spend in all? (Lesson 1C)
Lesson 2C Multiply Decimals 257
Multi-Part
Lesson
2
Multiply Decimals
PART
A
B
C
D
Problem-Solving Strategy:
Look for a Pattern
Main Idea I will solve problems by looking for a pattern.
Marvin is shopping for new
M
cclothes. He receives a
member discount on his
purchases. The table
shows the amount Marvin
pays for his clothes and the
amount of his discount.
Cost
Discount
Amount
Marvin
Pays
Shirt
$34.70
$3.47
$31.23
Pants
$48.50
$4.85
$43.65
Jacket
$62.30
$6.23
$56.07
Boots
$68.80
Item
Based on the pattern, how much will Marvin pay, and
how much will the discount be for boots that cost $68.80?
Understand
What facts do you know?
• Marvin receives a discount on his
purchased items.
• We know the cost of the boots.
What do you need to find?
• We need to find the amount Marvin will
pay for the boots and the amount of the discount.
Plan
One way to solve the problem is by looking for a pattern. Then, extend the
pattern to find the amount paid.
Solve
Use your plan to solve the problem.
If you multiply the cost of the item by 0.1, you can find the discount.
Subtract the discount from the total cost to find how much Marvin pays.
$68.80 × 0.1 = $6.88
$68.80 - $6.88 = $61.92
Check
The discount is $6.88.
Marvin pays $61.92.
The answer fits the pattern. So, it is correct. GLE 0506.2.5 Develop fluency in solving multi-step problems using whole numbers, fractions, mixed
numbers, decimals. GLE 0506.1.2 Apply and adapt a variety of appropriate strategies to problem solving,
including estimation, and reasonableness of the solution. Also addresses GLE 0506.1.5.
258
2
Multiply and Divide Decimals
Refer to the problem on the previous page.
1. What happens to the decimal point
when the cost of the item is multiplied
by 0.1?
3. Marvin only had $50 left to spend.
With his discount, would he be able
to purchase another shirt that costs
$54.70? Explain.
2. How much would the discount be if
Marvin bought a hat that cost $16.50?
4. Why was finding the pattern a helpful
strategy to find the cost of Marvin’s
discount?
EXTRA
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Solve. Use the look for a pattern strategy.
5. Every year, Victoria receives $30 for her
birthday, plus $2 for each year of her
age. Lacey receives $20 for her birthday
and $4 for each year of her age. In
2010, Victoria is 10, and Lacey is 6.
In what year will they both receive the
same amount of money?
6. Describe the pattern below. Then find
the next three numbers.
0.03, 0.3, 3, 30, , , 7. Draw the next two figures in the
pattern.
9. Algebra Copy and complete the
table. What is the pattern?
Input (x)
Output (y)
5
9
10
19
15
20
39
49
10. Adrienne did 13 sit-ups the first day,
20 sit-ups the second day, and
27 sit-ups the third day. If the pattern
continues, how many sit-ups will she
do on the sixth day?
11. Describe the pattern below. Then find
the next two numbers.
784.5, 78.45, 7.845, , 8. Samuel will arrive at the airport on the
first plane after 10 A.M. Airplanes arrive
every 50 minutes beginning at 6 A.M.
When will Samuel’s plane arrive?
12.
E
WRITE MATH Write a real-world
problem involving a pattern with
decimals. Give it to a classmate and
see if he or she can continue it.
Lesson 2D Multiply Decimals 259
Mid-Chapter
Check
Estimate each product. (Lesson 1A)
1. 4 × $3.14
2. 7 × $5.89
3. 3 × 6.3
4. 8 × 2.7
13. The dimensions of a swimming pool
are shown. Find the area of the pool.
(Lesson 1C)
5. The store sells newspapers for $1.75
each. Mrs. Horace wants to buy 24 for
her classroom. Estimate the total cost.
(Lesson 1A)
6. Renee ran 1.3 miles every day for one
week. About how many miles did she
run in one week? (Lesson 1A)
Multiply. (Lesson 1C)
7. 5 × 2.4
8. 9 × 6.7
9. 2 × 9.5
10. 7 × 4.8
11. The table shows a list of coins and the
average mass for that coin.
Coin
2.67
Nickel
5.01
Dime
2.28
Quarter
5.66
15. 7.5 × 3.6
16. 0.6 × 8.2
17. 0.06 × 7.4
18. Dale bought 10 apples at the store for
$0.49 each. How much did he pay for
all 10 apples? (Lesson 2C)
Find each product. (Lesson 2C)
19. 6.2 × 100
20. 45.7 × 0.1
21. 0.12 × 10
22. 92.3 × 0.01
23. Describe the pattern below. Then find
the next number. (Lesson 2D)
If Jeremy had 3 dimes and 2 quarters
in his pocket, what would be the total
mass of those coins? (Lesson 1C)
12. Find the area of the
parallelogram in
square meters.
260
14. 1.3 × 4.1
Mass (g)
Penny
(Lesson 2B)
Multiply. (Lesson 2B)
0.9 m
1.8 m
Multiply and Divide Decimals
0.732, 7.32, 73.2, 24.
E
WRITE MATH A stadium has
3,720 seats and one tenth, or 0.1, of
the seats are reserved for students.
Explain how to find how many seats
are reserved for students. Then solve.
(Lesson 2C)
Multi-Part
Lesson
3
PART
Divide Decimals by Whole Numbers
A
Main Idea
I will estimate
quotients of decimals
and whole numbers.
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, and decimals.
GLE 0506.1.2 Apply and adapt
a variety of appropriate
strategies to problem solving,
including estimation, and
reasonableness of the solution.
B
C
D
Estimate Quotients
of Decimals and
Whole Numbers
To estimate quotients of decimals and whole numbers, you can
use rounding and compatible numbers.
ANIMALS A live sponge is an animal
that lives in the ocean. Sponges filter
water to get food. One sponge can
filter 26.4 liters of water in 4 hours.
About how many liters of water can
a sponge filter in one hour?
26.4 ÷ 4
28 ÷ 4
28 ÷ 4 = 7
Change 26.4 to 28
because 28 and 4 are
compatible numbers.
Divide mentally.
So, a sponge can filter about 7 liters of water in one hour.
Use Compatible
Numbers
MONEY Ms. Glover buys 2 kites for a total of $15.18.
If each kite costs the same, about how much did each
kite cost? Explain why your answer is reasonable.
$15.18 ÷ 2
$16 ÷ 2
$16 ÷ 2 = $8
Change $15.18 to $16 because
16 and 2 are compatible numbers.
Divide mentally.
So, $15.18 ÷ 2 is about $8. Since 2 × 8 = 16 and 16 ≈ 15.18,
your answer is reasonable.
Lesson 3A Divide Decimals by Whole Numbers 261
Round Money
Rounding a decimal is
the same as rounding
a whole number.
To round $32.57 to
the nearest dollar,
look at the number
to the right. Since it
is 5, round $32.57
to $33.
RESTAURANT Three friends
went out to dinner. The total
cost of their meal was
$32.57. If the friends split
the bill evenly, about how
much will each person pay?
Explain why your answer
is reasonable.
$32.57 ÷ 3
$33 ÷ 3
$33 ÷ 3 = $11
Round $32.57 to the nearest whole
dollar amount.
Divide mentally.
Each friend would pay about $11. Since 3 × 11 = 33 and
33 ≈ 32.57, your answer is reasonable.
Use Rounding
Estimate 78.74 ÷ 42.
78.74 ÷ 42
80 ÷ 40
80 ÷ 40 = 2
Round 42 to 40. Replace 78.74 with 80
because 80 and 40 are compatible
numbers.
Divide mentally.
So, 78.74 ÷ 42 is about 2.
Estimate each quotient
quotient. See Examples 11–44
1. $19.50 ÷ 5
2. $47.25 ÷ 25
3. 16.8 ÷ 4
4. 87.3 ÷ 11
5. 44.7 ÷ 5
6. 195.8 ÷ 12
7. It costs $158.75 to purchase 15 tickets to the state fair. About
how much does one ticket cost?
8. Jake bought 3 drawing pens for $8.07. Each pen costs the
same amount. About how much did he spend for 1 pen?
9.
E
TALK MATH Describe the steps for estimating dividing
money by a whole number.
262
Multiply and Divide Decimals
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Estimate
E
ti t each
h quotient.
ti t See Examples 1–4
10. $28.20 ÷ 6
11. $7.92 ÷ 6
12. 88.3 ÷ 9
13. 128.9 ÷ 12
14. 576.4 ÷ 62
15. $15.47 ÷ 7
16. 56.3 ÷ 18
17. 32.17 ÷ 7
18. $175.32 ÷ 3
19. A canoe rental company offers two trips
along the river. Neil and Gabriela choose
the longer trip. If they split the cost of the
rental, about how much will each
person pay?
Canoe Rental
Trip
Distance (miles)
Cost
A
5.75
$12.98
B
8.5
$16.32
20. It costs $88.50 for 6 adults to see an exhibit on Egyptian mummies.
About how much does it cost 1 adult to see the exhibit?
21. Measurement There are 74.4 grams of sugar in 3 servings of
grapes. About how many grams of sugar are in a single serving?
Measurement
The table shows the density
of each object. Density describes how tightly the
particles in an object are packed together. You
can find density by dividing an object’s mass by
its volume.
Substance
Mass
(g)
Volume
(cm3)
Aluminum
13.5
5
Gold
56.7
3
121.5
9
Mercury
22. Estimate the density of aluminum.
23. Is the density of gold greater than the density
of mercury? Explain.
24. The density of gold is about how many times
greater than the density of aluminum?
25. OPEN ENDED Write a division problem involving money. Describe
the steps that you used to estimate the quotient.
26.
E
WRITE MATH Explain how to use compatible numbers
to estimate 39.12 ÷ 21.
Lesson 3A Divide Decimals by Whole Numbers 263
Multi-Part
Lesson
3
PART
Divide Decimals by Whole Numbers
A
Main Idea
I will explore dividing a
decimal by a whole
number.
B
C
D
E
Divide Decimals
by Whole Numbers
You can use place-value models to divide a decimal by a
whole number.
Materials
base-ten blocks
Find 3.6 ÷ 3 using models.
Step 1
Model 3.6 as 3 wholes and 6 tenths.
Step 2
Separate the blocks into three equal groups.
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, decimals.
Also addresses GLE 0506.1.4.
There is one whole and two tenths in each group.
So, 3.6 ÷ 3 = 1.2.
and Apply It
Use models to find each quotient.
1. 3.4 ÷ 2
2. 6.3 ÷ 3
3. 5.6 ÷ 4
4. 2.7 ÷ 3
5. 4.8 ÷ 2
6. 2.8 ÷ 4
7.
E
TALK MATH How could you solve Exercises 1–6 without
using models?
264
Multiply and Divide Decimals
Multi-Part
Lesson
3
PART
Divide Decimals
A
Main Idea
I will divide a decimal
by a whole number.
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, decimals.
Also addresses GLE 0506.1.7.
B
C
D
E
Divide Decimals
by Whole Numbers
As shown in the previous lesson, dividing a decimal by a whole
number is similar to dividing whole numbers.
RIBBON There are 8.4 meters left on
a roll of ribbon. Nancy wants to
cut the ribbon in half. What will
be the size of each piece of ribbon?
Find 8.4 ÷ 2. Estimate 8 ÷ 2 = 4
4.2
2 8.4
8
−−−
04
4
−−−
0
Place the decimal point directly above
the decimal point in the dividend.
So, 8.4 ÷ 2 = 4.2.
Each piece of ribbon will be 4.2 meters long.
Check 4.2 ≈ 4 Divide a Decimal
by a Two-Digit Number
Find 6.54 ÷ 12.
0.545
12 6.540
- 60
54
48
−−−−
60
60
−−−−
0
Place the decimal point.
Annex a zero and continue dividing.
6.54 ÷ 12 = 0.545
Lesson 3C Divide Decimals by Whole Numbers 265
When dividing decimals, sometimes the answer does not
come out evenly. You need to round the quotient to a
specified place-value position.
Round a Quotient
MONEY Corey bought 3 books at the book fair for $49.90.
If each book costs the same amount, what is the price of
each book? Round to the nearest cent.
x
You may need to anne
0s when dividing a
decimal by a whole
number.
Find $49.90 ÷ 3.
16.633
49.900
3 -3
19
18
−−−−
19
-18
10
9
−−−
10
9
−−−
1
Place the decimal point.
Divide until you place a digit in the
thousandths place, so you can round to the
nearest cent.
The cost of each book is $16.63.
Divide. Round to the nearest tenth if necessary
Divide
necessary. Examples 11–33
1. 3 48.33
2. 2 8.8
3. 4 8.43
4. 145.8 ÷ 12
5. 22.11 ÷ 11
6. 65.9 ÷ 14
7. 18 38.4
8. 14 3.66
9. 15 36.16
10. Mandy and 5 of her friends bought a package of
bottled water for $4.98. How much will each friend
pay to the nearest cent, if the cost is divided equally?
11.
E
TALK MATH Is the quotient 9.3 ÷ 10 greater than one
or less than one? Explain.
266
Multiply and Divide Decimals
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Divide.
Di
id R
Round
d tto th
the nearestt ttenth
th if necessary. Examples 1–3
12. 12.4 ÷ 9
13. 14.14 ÷ 14
14. 55.44 ÷ 11
15. 7 7.21
16. 4 6.28
17. 6 276.2
18. 380.5 ÷ 30
19. 75.2 ÷ 24
20. 4.68 ÷ 22
21. 42 223.6
22. 20 8.14
23. 12 361.5
24. Four girls swam the 4-by-200 meter freestyle relay in a total
of 540.5 seconds. If each girl swam their part of the race in
the same amount of time, what was the time for one girl?
25. The table shows the prices for two packs
of batteries. Which pack is a better buy?
Explain your reasoning.
26. The total cost of four movie tickets is $33.40
What is the cost of one ticket?
Batteries
Pack
Number of
Batteries
Price
A
B
4
6
$2.44
$3.90
Use the information to solve the problem.
27. How much money do they each make working together if the
money is split evenly?
28. OPEN ENDED Write a real-life problem that involves dividing a
decimal by a whole number.
29.
E
WRITE MATH Why is rounding important when dividing
a decimal by a whole number?
Lesson 3C Divide Decimals by Whole Numbers 267
Multi-Part
Lesson
3
Divide Decimals by Whole Numbers
PART
A
Main Idea
I will divide a decimal
by powers of ten.
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, decimals.
B
C
D
E
Divide Decimals
by Powers of Ten
Dividing a decimal by a power of 10 moves the decimal point to
the left the same number of places as the number of zeros in
the power of 10.
Decimal
Power of Ten
Quotient
53.7
÷1
= 53.7
53.7
÷ 10
= 5.37
53.7
÷ 100
= 0.537
53.7
÷ 1,000
= 0.0537
Laura will need to make
10 payments to pay for her
new motorized scooter.
How much will each payment
be if the scooter cost $219.60?
Find $219.60 ÷ 10.
$219.60 ÷ 10 = 219.60 10 has one zero. Move the decimal
= $21.96
point 1 place to the left.
So, each payment will be $21.96.
Divide by a Power of Ten
36.4 ÷ 1,000
36.4 ÷ 1,000 = 036.4 1,000 has three zeros. Move the
decimal point 3 places to the left.
= 0.0364 Insert a leading zero.
So, 36.4 ÷ 1,000 = 0.0364.
268
Multiply and Divide Decimals
The quotient of a
number and a power
of ten that is greater
than 1 will always
be less than the
original number.
SCIENCE In the past 100 years, scientists measured the
movement of the continents to be 190.5 centimeters.
If the continents moved the same amount each year, how
much did the continents move in one year?
Divide the total distance moved by 100.
190.5 ÷ 100 = 1.905 100 has 2 zeros. So move the
decimal point 2 places to the left.
= 1.905
The continents moved 1.905 centimeters each year.
Find each quotient
quotient. Examples 11–33
1. 7.2 ÷ 10
2. 21.5 ÷ 100
3. 19.2 ÷ 1,000
4. 10 14.7
5. 100 5.62
6. 100 18.7
7. 6.3 ÷ 1,000
8. 0.05 ÷ 1
9. 0.012 ÷ 100
10. 100 8.72
12. 100 98.6
11. 10 2.46
13. Herbert bought red beans to make chili to
sell at a fundraiser. The total price of the red
beans was $13.90. How much did it cost for
each can?
Items Purchased
Item
Quantity
red beans
shredded
cheese
10
6
14. Sarah was trying to decide what kind of cat food to buy at the
store. Smiley Cat costs $7.90 for 10 pounds. Purr Plus costs $0.85
per pound. Which brand is the better buy? Explain your reasoning.
15.
E
TALK MATH Suppose you want to find the number of
10-millimeter ribbons that can be cut from a ribbon that is
192.6 millimeters long. Explain how you can mentally find the
number of ribbons that can be cut.
Lesson 3D Divide Decimals by Whole Numbers 269
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Begins on page EP2.
Find
Fi
d each
h quotient.
ti t Examples
l 1–3
16. 8.3 ÷ 100
17. 208 ÷ 100
18. 5.71 ÷ 1
19. 1 0.07
20. 1,000 437
21. 1,000 32.7
22. 0.4 ÷ 100
23. 102.6 ÷ 100
24. 78.2 ÷ 10
25. 10 5.4
26. 100 2.1
27. 1,000 0.75
28. Christy purchased 6.75 pounds of licorice. How much licorice does
she need to put in each bag if she divides the total amount into
10 equal-sized bags?
For Exercises 29–31, use the table at the right.
29. Each row of the grocery store parking lot
has 10 parking spots of equal width.
What is the width for each spot?
30. How much space is given for each
parking spot at the mall parking lot if
each spot has an equal width?
Number of
Parking Spots
per Row
Combined Width
of all Parking
Spots (m)
Grocery Store
10
31.92
Hardware Store
10
31.96
Mall
10
31.30
Location
31. Which location gives the greatest space for each parking spot?
32. In Alaska, scientists are studying the melting of glaciers. They found
that in the past 10 years, the glaciers receded about 59.05 feet.
If the glaciers receded at the same rate, how much did they recede
in one year?
33. WHICH ONE DOESN’T BELONG? Identify the expression that does
not belong with the other three. Explain your reasoning.
6.7 ÷ 10
4 ÷ 1,000
0.2 ÷ 1
52.1 ÷ 100
34. CHALLENGE Tell what number you must divide 180 by to get 1.8.
35.
E
WRITE MATH Describe the relationship between the number
of places a decimal is moved to the left and the change in the
value of the number.
270
Multiply and Divide Decimals
Estimation Roll Off
Estimate Dividing a Decimal by a Whole Number
Get Ready!
Players: 2, 3, or 4 players
Get Set!
Each group will need two
number cubes, paper,
and pencil.
You will need: 2 number cubes, paper
and pencil
The player with the most
correct estimates is the
winner for that round.
Roll the cubes to continue
play as time permits.
Go!
Roll both number cubes.
The sum of the cubes will
be the quotient.
Each player will have
5 minutes to write down as
many division equations
as possible with an estimate
that equals the sum of the
numbers rolled on the
number cubes. At least one
of the numbers in the
equation must be a decimal.
At the end of five minutes,
share the equations with the
rest of the group and tally
the number of equations
with correct estimates.
Game Time Estimation Roll Off
271
Multi-Part
Lesson
4
PART
Divide Decimals
A
Main Idea
I will explore using
models to divide a
decimal by a decimal.
B
C
D
E
Divide Decimals
Using Models
You can use models to divide decimals by decimals.
Materials
base-ten blocks
Find 2.4 ÷ 0.8.
Step 1
Model 2.4 using two wholes and four tenths.
Get ConnectED
1
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, decimals.
Also addresses GLE 0506.1.4.
1
0.4
Step 2
Since you are dividing by tenths, replace both of
the ones blocks with tenths.
Step 3
Separate the tenths into groups of eight tenths to
show dividing by 0.8.
0.8
0.8
0.8
3 groups
There are three groups of eight tenths in 2.4.
So, 2.4 ÷ 0.8 = 3.
272
Multiply and Divide Decimals
Model 0.3 ÷ 0.06.
Step 1
Model 0.3 using 3 tenths.
Step 2
Replace the tenths with hundredths
since you are dividing by hundredths.
Step 3
Separate the hundredths into groups of
6 hundredths to show dividing by 0.06.
5 groups
There are 5 groups of 6 hundredths in 0.3.
So, 0.3 ÷ 0.06 = 5.
and Apply It
Use models to find each quotient.
1. 2.4 ÷ 0.3
2. 1.6 ÷ 0.4
3. 1.8 ÷ 0.9
4. 0.2 ÷ 0.04
5. 0.4 ÷ 0.05
6. 0.2 ÷ 0.02
7. Grace purchased some packages of gum for $1.50. If each package
costs $0.50, how many packages did Grace purchase?
8. Tell why the quotient 0.9 ÷ 0.09 is a whole number. What does the
quotient represent?
9.
E
WRITE MATH Refer to Activity 2. Explain why in Step 2 you
replaced the tenths with hundredths.
Lesson 4A Divide Decimals 273
Multi-Part
Lesson
4
Divide Decimals
PART
A
Main Idea
I will divide decimals
by decimals.
Get ConnectED
GLE 0506.2.5
Develop fluency in solving
multi-step problems using
whole numbers, fractions,
mixed numbers, decimals.
B
C
D
E
Divide Decimals
When dividing by decimals, change the divisor into a whole
number. To do this, multiply both the divisor and the dividend
by the same power of 10. Then divide as with whole numbers.
TRAVEL The Prease family drove
213.9 miles to the beach. Their
car used 9.3 gallons of gas. How
many miles did they drive per
gallon of gas?
Find 213.9 ÷ 9.3.
Multiply 9.3 by 10 to
make a whole number.
23.
9.3 213.9
93 2,139.
1 86
−−−−−
279
Multiply 213.9 by the
279
same number, 10.
−−−−
0
So, they drove 23 miles per gallon
Place the decimal point.
Divide as with
whole numbers.
of gas.
Divide Decimals
Find 5.32 ÷ 1.4.
Multiply 1.4 by 10 to
make a whole number.
1.4 5.32
Multiply 5.32 by the
same number, 10.
3.8
14 53.2
- 42
11 2
- 11 2
0
So, 5.32 ÷ 1.4 = 3.8.
Check 3.8 × 1.4 = 5.32 274
Multiply and Divide Decimals
Place the decimal point.
Divide as with whole numbers.
Sometimes it is necessary to annex a zero in the quotient
and/or the dividend.
Zeros in the Quotient and Dividend
Find 26.4 ÷ 0.22.
26.40
0.22 Multiply each by 100.
120.
22 2,640.
- 22
44
44
−−−−
00
Place the decimal point.
Divide.
Write a zero in the ones
place of the quotient
because 0 ÷ 22 = 0.
So, 26.4 ÷ 0.22 = 120
Check 120 × 0.22 = 26.4 Find 0.06 ÷ 1.5.
0.06
1.5 Adding a zero to the
end of a decimal does
not change the value
of the decimal.
0.6 = 0.60
Multiply each by 10.
0.04
15 0.60
- 0
60
60
−−−−
0
Place the decimal point.
15 does not go into 6, so
write a 0 in the hundredths
place.
Annex a 0 to continue.
So, 0.06 ÷ 1.5 is 0.04.
Check 0.04 × 1.5 = 0.06 Divide. Examples 11–44
Divide
1. 6.89 ÷ 1.3
2. 4.58 ÷ 0.5
3. 0.66 ÷ 0.3
4. 16.5 ÷ 0.03
5. 0.462 ÷ 0.2
6. 18.6 ÷ 0.12
7. 0.07 ÷ 1.4
8. 3.822 ÷ 0.04
9. 0.08 ÷ 1.6
10. Mrs. Chibas is making chocolate chip cookies
for her daughter’s class. She bought
a tub of chocolate chip cookie dough that
contained 57.6 ounces of dough. If each
cookie needs 1.2 ounces of dough, how
many cookies can she make?
11.
E
TALK MATH Explain how to solve 0.808 ÷ 0.4.
Lesson 4B Divide Decimals 275
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Divide.
Di
id Examples
l 1–4
12. 14.4 ÷ 0.4
13. 13.2 ÷ 0.3
14. 3.51 ÷ 0.78
15. 84.78 ÷ 0.15
16. 0.92 ÷ 0.4
17. 12.42 ÷ 4.6
18. 0.242 ÷ 0.4
19. 1.404 ÷ 0.45
20. 0.4 ÷ 0.05
21. 29.12 ÷ 1.3
22. 7.98 ÷ 4.2
23. 2.07 ÷ 0.9
24. Measurement Kaya works for a T-shirt company
and has 49.5 yards of fabric to make specialty T-shirts.
If each T-shirt needs 4.5 yards of fabric, how many
T-shirts can she make?
25. A pizza chef can make one pizza in 52.3 seconds.
How many pizzas can the pizza chef make in 418.4 seconds?
26. Sei paid $5,787.28 in rent for a certain number of months. If the
cost of rent for one month is $723.41, how many months has Sei
already paid?
27. Kasey is 4.5 feet tall. Her brother, Jerome, is 6.75 feet tall. How
many times taller is Jerome than Kasey?
28. OPEN ENDED Write a real-world problem that involves dividing
a decimal by a decimal.
29. NUMBER SENSE Without solving, would 1.98 ÷ 0.51 be closer to
4 or 5? Explain.
30. FIND THE ERROR Sonia is finding 13.2 ÷ 2.2.
Help find and correct her mistake.
13.2
2.2 31.
E
0.6
22 13.2
13 2
−−−−−
0
WRITE MATH Explain how you can check your answer when
dividing decimals.
276
Multiply and Divide Decimals
Test Practice
32. Lamar spent $16.25 on peanuts. If he
bought 2.6 pounds of peanuts, how
much does 1 pound of peanuts cost?
34. The area of the rectangle is
335.62 square inches. If the length is
34.6 inches, what is the width?
34.6 in.
A. $5.55
C. $6.55
B. $6.25
D. $7.25
33. Mason has 1.71 meters of string to
decorate his locker. He cut the string
into 0.19-meter lengths. How many
pieces does he have?
F. 6
H. 8
G. 7
I. 9
35.
A. 8.6 inches
C. 10.3 inches
B. 9.7 inches
D. 10.9 inches
SHORT RESPONSE Patricia has
3.75 pounds of hamburger. She is
making hamburgers with 0.25 pound
of hamburger each. How many
hamburgers can she make?
Divide. (Lesson 3D)
36. 10 46.33
37. 100 48.3
38. 1,000 9,435.2
39. Mr. Ginobli pays the same amount each month on a loan. In one
year, he paid a total of $1,276.20. How much did Mr. Ginobli pay
each month for the bank loan? (Lesson 3C)
Find each product. (Lesson 2C)
40. 52.8 × 100
41. 3.87 × 10
42. 0.26 × 1,000
43. 73.54 × 0.1
44. 6.02 × 0.01
45. 132.49 × 0.001
46. The flag at the right is the flag
of Switzerland. What is the area
of the flag? (Lesson 2B)
3.15 m
4.5 m
Lesson 4B Divide Decimals 277
Multi-Part
Lesson
4
PART
Divide Decimals
A
C
B
Problem-Solving Investigation
Main Idea I will choose the best strategy to solve a problem.
Blake measured the amount of rain each
.
day for five days for his first experiment.
Rain Experiment
Day
Amount (in.)
Monday
Tuesday
Wednesday
Thursday
Friday
1.2
0.5
2.4
3.75
1.0
Then, Blake measured
the amount of rain for
another five days for
a second experiment.
It rained the same total amount as
the first experiment, but this time
it rained an equal amount each day.
YOUR MISSION: Determine how much it rained each day in
the second experiment.
Understand
What facts do you know?
• the amount it rained each day for the first experiment
• the total amount of rain for each experiment is the same
What do you need to find?
• how much it rained each day for the second experiment
Plan
Solve
Solve by making a diagram.
1.2 + 0.5 + 2.4 + 3.75 + 1.0 = 8.85 total amount of rain
8.85
in Experiment 1
Think: What is 8.85 ÷ 5?
8.85 ÷ 5 = 1.77
So, it rained 1.77 inches each day of Experiment 2.
Check
Since 1.77 × 5 = 8.85, the answer is reasonable. GLE 0506.2.5 Develop fluency in solving multi-step problems using whole numbers, fractions, mixed numbers,
and decimals. GLE 0506.1.2 Apply and adapt a variety of appropriate strategies to problem solving, including
estimation, and reasonableness of the solution.
278
Multiply and Divide Decimals
EXTRA
%
)# E
# T4 IC
!C
2A
0R
P
Begins on page EP2.
•
•
•
•
Determine reasonable answers.
Look for a pattern.
Draw a diagram.
Choose an operation.
Use any strategy shown to solve each
problem.
1. Musa wants to buy 3 pairs of pants for
$39.54 each and 2 shirts for $17.99
each. Does she need to save $170,
$160, or $150?
5. Kristen wants to buy a new skateboard.
So far, she has saved $31.26 and
$45.50 from her two lawn-mowing
jobs. How much more money does she
need to buy the skateboard if it costs
$131.99?
6. Teresa can spend $10 on food. Which
of the following combination of foods
can she NOT buy?
• hamburger and fruit salad
• 2 fruit salads and ice cream
• hamburger and ice cream
2. NUMBER SENSE Describe the pattern
below. Then find the next three numbers.
Item
Price
2.54, 2.6, 2.66, 2.72, , , Ice cream
Hamburger
Fruit Salad
$3.29
$6.79
$2.25
3. Victor bought a small pizza at Pizza
Palace. The price of an extra large pizza
is equal to 2 times the price of a small
pizza plus $3. How much did Victor pay
for the pizza?
7. BAR DIAGRAM Brandon ran 21.6 laps
over three days. If he ran the same
amount each day, how many laps did
he run each day?
8. Thomas noticed that for every 4 cars
that went through a car wash, he saw
2 trucks, if 24 vehicles went through
the car wash, how many were trucks?
4. Anne is setting up tables for a conference.
She is putting 5 rectangular tables end-toend to make one large table. One
rectangular table can seat one person at
each end and 2 people on each side.
How many people will be able to sit
around the new large table?
9. Measurement The width of a
swimming pool is 18.6 yards and
divided into 6 equal rows. What is the
width of each row?
10.
E
WRITE MATH What strategy did you
use to solve Exercise 4? Explain why
your strategy is appropriate to solve
the problem.
Lesson 4C Divide Decimals 279
The Sun is amazing. It is a star that
is 4.5 billion years old. At its center,
the temperature is 27 million
degrees Fahrenheit. That’s about
67,000 times hotter than an oven!
The Sun is not only incredibly hot,
but also very large. If it was hollow,
1,000,000 Earths could fit inside
of it. Because the Sun is so big,
it has a lot of gravity. This gravity
pulls on the 8 planets and keeps
them in orbit.
Planet
280
Average
Distance from
Sun (miles)
Each planet’s orbit is a different
shape. Orbital eccentricity describes
the shape of a planet’s orbit.
Scientists use decimals to measure
orbital eccentricity. If a planet’s
orbit is perfectly circular, its orbital
eccentricity is 0.0. The more ovalshaped the planet’s orbit, the closer
the decimal is to 1.0. Because each
orbit is different, the planets are
not always the same distance from
the sun. Scientists describe these
distances from the sun as averages.
Orbital
Eccentricity
Gravitational
Pull, ( meters )
_
second2
Mercury
35,983,093
0.205
3.59
Venus
67,237,910
0.007
8.87
Earth
92,955,820
0.017
9.81
Mars
141,633,330
0.055
3.77
Jupiter
483,682,810
0.094
25.95
Saturn
886,526,100
0.057
11.08
Uranus
1,783,935,996
0.046
10.67
Neptune
2,795,084,800
0.011
14.07
Multiply and Divide Decimals
Use the information on the previous page to solve each problem.
1. The gravitational pull of Neptune is
about how many times larger than
the gravitational pull of Mercury?
2. The gravitational pull of Jupiter is
about how many times larger than
the gravitational pull of Mars?
3. Which planet’s orbital eccentricity is
about 4 times the amount of
Neptune’s orbital eccentricity?
4. The gravitational pull of Uranus is
about 1.25 times larger than what
planet?
5. The gravitational pull of Earth is
about 2.5 times larger than what
planet?
6. Based on the gravitational pull on
each planet, would you expect to
weigh more or less on Mercury?
Explain your answer.
If you drove
60 miles per hour,
it would take you
176 years to get to
the Sun.
Problem Solving in Science 281
Chapter Study
Guide and Review
Be sure the following Key
Concepts are written in your
Foldable.
Vocabulary
powers of 10
Vocabulary Check
M
Div ultip
ide ly a
De nd
cim
als
Key Concepts
Multiply Decimals (Lessons 1 and 2)
• To multiply decimals, multiply as with
whole numbers. The product has the same
number of decimal places as the sum of the
number of decimal places in each factor.
Choose the correct term or number
to complete each sentence.
1. The product of 4.63 × (0.01, 100 )
is 463.
2. To mentally divide 8.3 by 1,000,
move the decimal point three
places to the (left, right).
3. When multiplying decimals and
placing the decimal point, find the
(sum, product) of the number of
decimal places in each factor.
Divide Decimals (Lessons 3 and 4)
• To divide decimals, change the divisor into
a whole number. Place the decimal point
directly above the decimal point in the
dividend, then divide as with whole
numbers.
Powers of Ten (Lessons 2 and 3)
To . . .
move the decimal point
to the . . .
multiply by a power
of 10 less than 1
left
multiply by a power
of 10 greater than 1
right
divide by a power of
10 less than 1
right
divide by a power of
10 greater than 1
left
282
Multiply and Divide Decimals
4. The quotient of 45.8 ÷ 0.01 is
(458, 4,580).
5. When dividing decimals, place the
decimal point in the quotient
directly above the decimal point
in the (dividend, divisor).
6. A pattern using (powers, factors) of
ten is used in dividing 4.19 ÷ 10.
7. The quotient of 3.6 ÷ 0.6 is the
same as the quotient of
36 ÷ (0.06, 6 ).
8. Numbers that are easy to divide
mentally are called (compatible,
decimal) numbers.
Multi-Part Lesson Review
Lesson 1
Multiply Decimals by Whole Numbers
Estimate Products of Whole Numbers and Decimals
Estimate each product.
9. 6 × 6.1
11. 4 × $9.21
10. 8 × 0.8
12. 3 × $5.89
13. A bus travels 55 miles per hour for
2.75 hours. Estimate the number of
miles driven.
EXAMPLE 1
Estimate the product of 25 × 4.7.
25 × 4.7
Round 4.7 to 5.
25 × 5
25 × 5 = 125
Multiply.
So, 25 × 4.7 is about 125.
Multiply Decimals by Whole Numbers
Multiply.
(Lesson 1A)
(Lesson 1C)
EXAMPLE 2
14. 6.2 × 5
15. 3 × 4.2
Find 2.6 × 8.
16. 0.08 × 13
17. 2.09 × 20
2.6
× 8
−−−−
20.8
18. How much would five breakfast cereal
bars cost?
one decimal place
Count one decimal
place from right to left.
So, 2.6 × 8 is 20.8.
Lesson 2
Multiply Decimals
Multiply Decimals
(Lesson 2B)
Multiply.
EXAMPLE 3
19. 0.3 × 2.5
20. 3.6 × 6.1
21. 0.08 × 3.4
22. 3.5 × 7.2
23. A rectangular patio measures 8.5 feet
by 10.75 feet. What is the area of the
patio in square feet?
Find 8.4 × 4.2.
8.4
×
4.2
−−−−
16 8
+
336
0
−−−−−
35.28
one decimal place
one decimal place
two decimal places
Chapter Study Guide and Review 283
Chapter Study Guide and Review
Lesson 2
Multiply Decimals
(continued)
Multiply Decimals by Powers of Ten
(Lesson 2C)
Find each product.
EXAMPLE 4
24. 0.5 × 100
Find 5.8 × 1,000.
5.8 × 1,000 = 5800.
25. 6.3 × 0.1
= 5,800
26. 47.8 × 0.01
So, 5.8 × 1,000 = 5,800.
27. 0.87 × 1,000
EXAMPLE 5
1,000 has
3 zeros, so
move the
decimal point
3 places to
the right.
Find 6.7 × 0.01.
28. The local sports store sold 100 boxes
of golf balls in the past week for $7.49
each. What was the total cost?
29. A remote control car with a speed of
2.7 feet per second was recently
modified to go 10 times faster. What is
the new speed of the car?
6.7 × 0.01 = 0.067
= 0.067
So, 6.7 × 0.01 = 0.067.
Problem-Solving Strategy: Look for a Pattern
There are
2 places after
the decimal
point, so move
the decimal
point 2 places
to the left.
(Lesson 2D)
Solve. Use the look for a pattern strategy.
EXAMPLE 6
30. Find the next three numbers.
Find the pattern in the table.
48.5, 47, 45.5, 44, , , 31. Draw the next figure in the pattern.
Input (x)
Output (y)
3
7.8
6
15.6
9
23.4
12
31.2
Study the relationship between each input
and output. Each output is 2.6 times
the input.
So, the pattern is 2.6 times x, or 2.6x.
284
Multiply and Divide Decimals
Lesson 3
Divide Decimals by Whole Numbers
Estimate Quotients of Decimals and Whole Numbers
Estimate each quotient.
(Lesson 3A)
EXAMPLE 7
32. 35.9 ÷ 9
33. 4.6 ÷ 4
Estimate the quotient of 37.1 ÷ 6.
34. 9.4 ÷ 3
35. 63.2 ÷ 7
37.1 ÷ 6
36. The amount of miles an athlete ran in
a week was 27.3 miles. What was the
approximate number of miles the
athlete ran per day, if he ran the same
amount each day?
36 ÷ 6 = 6
Divide mentally.
So, 37.1 ÷ 6 is about 6.
Divide Decimals by Whole Numbers
Divide.
36 ÷ 6
Change 37.1 to 36
because 36 and 6 are
compatible numbers.
(Lesson 3C)
EXAMPLE 8
56.4
37. 4 38. 8 4.52
Find the quotient of 12.6 ÷ 7.
39. 67.2 ÷ 5
40. 84.7 ÷ 7
1.8
12.6
7 7
−−−
56
56
−−−−
0
41. Marty spent $20.93 for baseball cards
over the past week. If he bought one
pack per day and each pack of cards is
the same price, how much does each
pack of cards cost?
Divide Decimals by Powers of Ten
Find each quotient.
Place the decimal point.
So, 12.6 ÷ 7 = 1.8.
(Lesson 3D)
EXAMPLE 9
42. 71.6 ÷ 0.1
43. 5.14 ÷ 0.01
Find 46.8 ÷ 100.
44. 28.7 ÷ 1,000
45. 309 ÷ 100
46.8 ÷ 100 = 0.468
46. The smaller glass holds 10 times less
than the larger glass. How many
milliliters does the smaller glass hold?
= 0.468
100 has 2 zeros,
so move the
decimal point
2 places to the left.
So, 46.8 ÷ 100 = 0.468.
V = 83.4 mL
V = ? mL
Chapter Study Guide and Review 285
Chapter Study Guide and Review
Lesson 4
Divide Decimals
Divide Decimals
(Lesson 4B)
Divide.
47. 3.96 ÷ 0.6
EXAMPLE 10
48. 22.26 ÷ 4.2
49. 0.525 ÷ 1.5
50. 4.2 ÷ 0.6
51. 48.38 ÷ 8.2
52. 0.063 ÷ 0.3
53. Stacey cut the board below into
12.6-inch pieces. How many boards
did she cut?
Find 18.6 ÷ 0.2.
18.6
0.2 Multiply 0.2 by 10 to make a
whole number. Multiply
18.6 by the same number, 10.
93.
2. 186.
18
−−−−
6
6
−−−
0
Place the decimal point.
Divide as with whole
numbers.
So, 18.6 ÷ 0.2 = 93.
Check 93 × 0.2 = 18.6 Problem-Solving Investigation: Choose the Best Strategy
Solve.
(Lesson 4C)
EXAMPLE 11
54. George, Francine, and Alisha spent
$45.75 on a birthday gift for their dad.
If they equally divided the price, how
much did each person pay?
Jamal rode his bike 5.7 miles over
3 days. If he rode his bike the same
amount each day, how far did he ride
in one day?
5.7 miles
55. Randy bought 4 pencils and a pad of
notebook paper. If each pencil cost
$0.30, how much did he spend in all?
?
5.7 ÷ 3 = 1.9
So, Jamal rode his bike 1.9 miles each day.
$1
.49
286
Multiply and Divide Decimals
Practice
Chapter Test
Estimate each product.
1. 7 × 0.9
2. 12 × 1.7
3. 5 × $2.79
4. 3 × $21.35
5. What is the area of the rectangle in
square centimeters?
4.8 cm
12. Melissa and her 3 friends went to the
movies and spent $40.25 on tickets,
popcorn, and a drink. About how much
will each person pay if they divide the
total price equally?
13. Toby and his 5 friends ordered a large
pizza for $15.99, and 6 large drinks for
$1.99 each. What is the total cost, not
including tax?
15.5 cm
Divide.
Multiply.
6. 7.2 × 0.5
8. 7.06 × 6.1
14. 5.7 ÷ 3
15. 0.2 ÷ 5
16. 4.8 ÷ 6
17. 10.5 ÷ 3
7. 2.8 × 3.1
9. 0.04 × 19.3
10. The table shows a list of recycling
prices per pound for certain metals.
Metal
Price per
pound ($)
Aluminum
0.92
Copper
2.04
Lead
0.68
Tin
6.67
Bridget collected 100 pounds of
aluminum cans to recycle. How much
money would she earn from collecting
the cans?
11. How many cubes will the next figure
have if the pattern below continues?
18. Ten bananas contain 290.5 grams of
carbohydrates. If each banana contains
the same amount of carbohydrates,
then how many grams of carbohydrates
are in one banana?
Divide.
19. 5.98 ÷ 4.6
20. 2.36 ÷ 0.4
21. 88.4 ÷ 6.8
22. 18.45 ÷ 2.05
23. Tracy paid $157.50 for concert tickets.
If each ticket costs $15.75, how many
tickets did she buy?
24.
E
WRITE MATH Explain the advantages
and disadvantages of using an estimate
when computing with decimals.
Practice Chapter Test
287
Test Practice
Mitch had $3.45 left after buying some supplies for
school. If he originally had 10 times that amount,
how much money in dollars did he have before he
bought supplies?
Read the Test Item
Be sure to count all of the
decimal places in the
numbers you are multiplying
before placing the decimal in
your answer.
You need to multiply the remaining amount of
money by ten to determine how much money he
started with.
Solve the Test Item
Multiply 3.45 by 10 to find the amount of money he
started with.
3.45
×
10
−−−−
34.50
two decimal places
two decimal places
Check your work.
34.50 ÷ 10 = 3.45
Fill in the grid.
34
.
50
Read each question. Then fill in the correct answer on the answer
sheet provided by your teacher or on a sheet of paper.
1. Monica downloaded 8 new songs that
cost $0.99 each. How much did
Monica spend for the songs she
downloaded?
2. Find the area of the parallelogram in
square centimeters by multiplying
base by height.
6.2 cm
A. $6.89
13.7 cm
B. $7.72
C. $7.92
D. $8.00
288
Multiply and Divide Decimals
F. 84.94
G. 78.92
H. 42.47
I. 19.9
3. The table shows Mr. Davidson’s monthly
water bill for June through September.
He splits the bill equally among
3 people. How much will each person
have to pay for the month of June?
Monthly Water Bill
7. About 12.4 million citizens in California
speak Spanish as their first language.
About 3 million citizens in Florida speak
Spanish as their first language. How
many more people speak Spanish in
California than in Florida?
Bill ($)
A. 12.1 million
C. 9.4 million
June
32.76
B. 10.4 million
D. 8.6 million
July
24.58
August
24.89
September
26.43
Month
A. $5.46
C. $8.81
8. How many places are to the right of the
decimal point in the product of the
following problem?
B. $8.19
D. $10.92
45.929 × 1.7
4. The History Museum is selling tickets at
the prices shown below.
Tickets
Price
Adult
$16.50
Children
$11.50
If a family purchases two adult tickets
and two children tickets, how much will
they spend for the tickets?
5.
6.
F. $23.00
H. $56.00
G. $33.00
I. $66.00
SHORT RESPONSE A family is
hiking a trail that is 627 yards long.
What is this distance in feet? (Hint:
1 yard equals 3 feet.)
F. 1 place
H. 3 places
G. 2 places
I. 4 places
9. Mary bought one of each item shown
below. What was the total price for all
of the items bought?
.59
$1
10.
GRIDDED RESPONSE A piece of
ribbon 3.2 meters long is cut into
0.4-meter pieces. How many pieces will
there be?
.49
$2
A. $5.07
C. $5.99
B. $5.79
D. $6.07
.99
$1
SHORT RESPONSE Mrs. Neal’s
class found the mass of the class gerbil
to be 96.3 grams. Each day, the gerbil
eats 0.1 of its body weight in food.
How much food does the gerbil eat?
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9
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6-1C
6-2B
6-3C
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6-4B
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6-2C
GLE 2.5 GLE 2.5 GLE 2.5 GLE 2.5 GLE 2.5 GLE 2.5 GLE 2.5 GLE 2.5 SPI 2.5 GLE 2.5
Test Practice 289