Name
3.7
?
Number and
Operations—5.3.E
Also 5.3.A
MATHEMATICAL PROCESSES
5.1.F
Multiply Decimals
Essential Question
What strategies can you use to place a
decimal point in a product?
Connect You can use what you have learned about patterns and
place value to place the decimal point in the product when you
multiply two decimals.
Remember
Think about the pattern on
the left. When a number is
multiplied by a decimal, the
decimal point moves one place
to the left in the product
for each decreasing place value
being multiplied.
1 × 0.1 = 0.1
0.1 × 0.1 = 0.01
0.01 × 0.1 = 0.001
Unlock
Unlock the
the Problem
Problem
A male leopard seal is measured and has a length of 2.8 meters. A male elephant
seal is about 1.5 times as long. What length is the male elephant seal?
Multiply. 1.5 × 2.8
One Way Use place value.
STEP 1
Multiply as with whole numbers.
STEP 2
Place the decimal point.
Think: Tenths are being multiplied by tenths.
Use the pattern 0.1 × 0.1.
Place the decimal point so the value of the
28
× 15
_
140
+ 280
__
420
×0.1
×0.1
2.8 1 place value
× 1.5 1 place value
_
1 + 1, or 2 place values
×0.01
decimal is __.
© Houghton Mifflin Harcourt Publishing Company
So, the length of a male elephant seal is about _ meters.
• What if you multiplied 2.8 by 1.74? What would be the
place value of the product? Explain your answer.
Module 3
141
Another Way Use estimation.
You can use an estimate to place the decimal point in a product.
Multiply. 7.8 × 3.12
STEP 1
312
× 78
__
Estimate by rounding each factor to the nearest
whole number.
7.8 ×
3.12
× 7.8
__
3.12
_×_=_
STEP 2
Multiply as with whole numbers.
STEP 3
Use the estimate to place the decimal point.
Think: The product should be close to
your estimate.
7.8 × 3.12 = __
Share
Share and
and Show
Show
Place the decimal point in the product.
1.
3.62
× 1.4
__
Think: A hundredth is being multiplied
by a tenth. Use the pattern 0.01 × 0.1.
5068
2.
6.8
×
1.2
_
816
Estimate: 1 × 7 = _
Find the product.
0.9
× 0.8
_
4.
84.5
× 5.5
__
5.
2.39
× 2.7
__
Math Talk
Mathematical Processes
Explain how you might
know the place value of
the product for Exercise
5 before you solve.
142
© Houghton Mifflin Harcourt Publishing Company
3.
Name
Problem
Problem Solving
Solving
Practice: Copy and Solve Find the product.
6. 3.4 × 5.2
7. 0.9 × 2.46
8. 9.1 × 5.7
9. 4.8 × 6.01
10. 7.6 × 18.7
11. 1.5 × 9.34
12. 0.77 × 14.9
13. 3.3 × 58.14
14.
Write Math
In the multiplication problem
5.5 × 4.6, is the answer 25.3 or 25.30? Explain your reasoning.
Problem
Problem Solving
Solving
Write Math
Show Your Work
15. Analyze Charlie has an adult Netherlands dwarf
rabbit that weighs 1.2 kilograms. Cliff’s adult Angora
rabbit weighs 2.9 times as much as Charlie’s rabbit.
How much does Cliff’s rabbit weigh?
16. Multi-Step John has pet rabbits in an enclosure that
has an area of 30.72 square feet. The enclosure Taylor
is planning to build for his rabbits will be 2.2 times
as large as John’s. How many more square feet will
Taylor’s enclosure have than John’s enclosure?
© Houghton Mifflin Harcourt Publishing Company
17.
A zoo is planning a new building
for the penguin exhibit. First, they made a model
that was 1.3 meters tall. Then, they made a more
detailed model that was 1.5 times as tall as the first
model. The building will be 2.5 times as tall as the
height of the detailed model. What will be the
height of the building?
Module 3 • Lesson 7
143
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
18. Arnold is solving this multiplication problem: 8.12 × 4.7. Which of these
estimates can Arnold use to help him determine where the decimal
point belongs in the product?
A
80 × 40 = 3,200
B
8 × 5 = 40
C
800 × 4 = 3,200
D
800 × 5 = 4,000
19. Which multiplication problem will not give the same product
as 5.5 × 4.44?
A
5.5 × 4.44
B
0.55 × 44.4
C
55 × 0.444
D
0.55 × 0.444
20. Multi-Step Gina bought 2.5 pounds of peaches that cost $1.38 per
pound at the grocery store. Amy went to the local farmer’s market and
purchased 3.5 pounds of peaches at $0.98 per pound. Who spent more
money, and how much more?
A
Gina, $0.20
C
Amy, $0.20
B
Gina, $0.02
D
Amy, $0.02
TEXAS Test Prep
21. A vine in Mr. Jackson’s garden was 3.6 feet long. When it is measured
144
A
7.5 feet
C
5.7 feet
B
6.6 feet
D
7.56 feet
© Houghton Mifflin Harcourt Publishing Company
again, it is 2.1 times as long. How long is the vine?
Number and Operations—5.3.E
Also, 5.3.A
MATHEMATICAL PROCESSES 5.1.F
H o mewo rk
and Practice
3.7
Name
Multiply Decimals
Find the product.
1. 0.6 × 0.8
2. 18.2 × 2.2
3. 3.84 × 4.5
4. 1.9 × 4.3
5. 0.7 × 2.51
6. 6.2 × 3.2
7. 6.6 × 4.01
8. 5.7 × 13.4
9. 1.3 × 5.54
10. 2.4 × 8.35
11. 0.55 × 16.3
12. 4.7 × 38.12
14. 24.3 × 0.8
15. 7.07 × 12.3
16. 49.21 × 3.6
13. 8.9 × 7.6
Problem
Problem Solving
Solving
17. The width of Mr. Simm’s driveway is 9.2 meters.
© Houghton Mifflin Harcourt Publishing Company
The length is 3.4 times the width. What is the
length of the driveway?
18. A female orangutan at the zoo weighs
79.3 pounds. A male orangutan weighs
2.3 times as much as the female orangutan.
How much does the male orangutan weigh?
Module 3 • Lesson 7 145
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
for 7.24 × 3.9. Which of the following is a
reasonable estimate for the product?
A
700 × 40 = 28,000
B
700 × 3 = 2,100
C
7 × 4 = 28
D
70 × 40 = 2,800
21. Mrs. Jones plants two evergreen trees in
her yard. The first tree is 6.25 feet tall. The
second tree is 0.5 times as tall. How tall is
the second tree?
same product as 4.6 × 5.2?
A
0.46 × 52
B
4.6 × 0.52
C
46 × 5.2
D
0.46 × 5.2
22. Mr. Endo buys 13.6 gallons of gasoline.
He pays $3.95 per gallon. How much does
Mr. Endo spend on gasoline?
A
$53.72
A
3.255 feet
B
$17.55
B
6.125 feet
C
$9.65
C
3.125 feet
D
$39.00
D
6.750 feet
23. Multi-Step Maria makes a quilt with a width
of 2.7 meters. The length is 3.2 times the width.
The area of a rectangle is the length times
the width of the rectangle. What is the area of
Maria’s quilt?
146
20. Which multiplication problem will give the
A
8.64 square meters
B
23.328 square meters
C
5.90 square meters
D
27.648 square meters
24. Multi-Step At the butcher shop, Jason
bought 2.4 pounds of ground beef for
$5.20 per pound. He bought 3.2 pounds
of ground turkey for $2.90 per pound.
How much more did Jason spend on
beef than on turkey?
A
$3.20
B
$2.30
C
$21.76
D
$9.58
© Houghton Mifflin Harcourt Publishing Company
19. Javier uses estimation to check the product