Download 3.3, Multiplying Decimals with Whole Numbers

Name
3.3
?
Number and
Operations—5.3.E
Also, 5.3.A
MATHEMATICAL PROCESSES
5.1.A, 5.1.C
Multiplication with Decimals
and Whole Numbers
Essential Question
How can you use properties and place value to
multiply a decimal and a whole number?
Unlock
Unlock the
the Problem
Problem
In 2010, the United States Mint released a newly designed
Lincoln penny. A Lincoln penny has a mass of 2.5 grams.
If there are 5 Lincoln pennies on a tray, what is the total
mass of the pennies?
• How much mass does one penny have?
• Use grouping language to describe
what you are asked to find.
Multiply. 5 × 2.5
Estimate the product. Round to the nearest whole number.
5×_=_
Another Way
One Way
Use the Distributive Property.
Show partial products.
5 × 2.5 = 5 × ( _ + 0.5)
STEP 1 Multiply the tenths by 5.
2.5
×
5
_
= ( _ × 2) + (5 × _ )
=_+_
=_
Math Talk
2 ones and 5 tenths
STEP 2 Multiply the ones by 5.
2.5
×
5
_
2.5
← 5 × 2 ones = 10 ones, or 1 ten
STEP 3 Add the partial products.
Mathematical Processes
Explain how the solution
would be different if you
multiplied $5 × 2.5.
© Houghton Mifflin Harcourt Publishing Company
← 5 × 5 tenths = 25 tenths, or
2.5
× 5
_
2.5
+__
10
So, 5 Lincoln pennies have a mass of __ grams.
Module 3
117
Example Use place value patterns.
Having a thickness of 1.35 millimeters, the dime is the thinnest
coin produced by the United States Mint. If you stacked 8 dimes,
what would be the total thickness of the stack?
Multiply. 8 × 1.35
STEP 1
STEP 2
STEP 3
Write the decimal factor as a
whole number.
Multiply as with whole
numbers.
Place the decimal point.
Think: 0.01 of 135 is 1.35. Find 0.01 of
1,080 and record the product.
Think: 1.35 × 100 = 135
1.35
×
8
_
?
× 100
⎯⎯⎯→
× 100
⎯⎯⎯→
135
× 8
__
1,080
× 0.01
⎯⎯⎯→
× 0.01
⎯⎯⎯→
1.35
×
8
_
A stack of 15 dimes would have a thickness of __ millimeters.
Share
Share and
and Show
Show
Place the decimal point in the product.
1.
6.81
×
7
__
47 67
Think: The place
value of the decimal
factor is hundredths.
2.
3.7
×
2
_
74
3.
19.34
×
5
__
96 70
5.
4.5
×
8
_
6.
40.7
×
5
__
4.
6.32
×
3
__
Math Talk
Mathematical Processes
Explain how you can
determine if your answer to
Exercise 6 is reasonable.
118
© Houghton Mifflin Harcourt Publishing Company
Find the product.
Name
Problem
Problem Solving
Solving
Practice: Copy and Solve Find the product.
7. 8 × 7.2
8. 3 × 1.45
9. 9 × 8.6
10. 6 × 0.79
11. 4 × 9.3
12. 7 × 0.81
13. 6 × 2.08
14. 5 × 23.66
15.
Write Math
Julie multiplies 6.27 by 7 and claims
the product is 438.9. Explain without multiplying how you know Julie’s
answer is not correct. Find the correct answer.
Problem
Problem Solving
Solving
Use the table for 16–18.
16. Sari has a bag containing 6 half dollars. What is the
mass of the half dollars in Sari’s bag?
Coin
17. Felicia is running a game booth at a carnival. One of the
games requires participants to guess the mass, in grams,
of a bag of 9 dimes. What is the actual mass of the dimes
in the bag?
Nickel
5.00
Dime
2.27
Quarter
5.67
Half Dollar
Dollar
© Houghton Mifflin Harcourt Publishing Company
18.
Mass (in grams)
11.34
8.1
Multi-Step Chance has $2 in quarters. Blake has
$5 in dollar coins. Whose coins have the greatest mass? Explain.
Module 3 • Lesson 3 119
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
19. Apply A hummingbird weighs 5.8 grams. If the hummingbird eats
8 times its body weight each day, how much does the bird eat in four
days?
A
23.2 grams
B
46.4 grams
C
185.6 grams
D
464 grams
20. Use Symbols Which expression shows how to use the Distributive
Property to find 5.17 × 9?
A
5.17 + 9
B
9 × (5.1) + 7
C
9 × (5.1 + 7)
D
9 × (5 + 0.17)
21. Multi-Step The cost to park a car in a parking lot is $1.10 per hour.
Maleek parked his car for 4 hours on Monday, 4 hours on Tuesday,
and 4 hours on Wednesday. How much did he spend on parking in all?
A
$4.10
B
$4.40
C
$13.10
D
$13.20
TEXAS Test Prep
If he walks to school 5 days, how many miles will Milo have walked?
120
A
1,825 miles
B
18.25 miles
C
182.5 miles
D
1.825 miles
© Houghton Mifflin Harcourt Publishing Company
22. Every day on his way to and from school, Milo walks a total of 3.65 miles.
Number and Operations—5.3.E
Also, 5.3.A
MATHEMATICAL PROCESSES 5.1.A, 5.1.C
H o mewo rk
and Practice
3.3
Name
Multiplication with Decimals
and Whole Numbers
Find the product.
1. 4 × 7.12
2. 3 × 0.29
3. 8 × 2.19
4. 7 × 18.3
5. 5 × 9.29
6. 2 × 42.1
7. 7 × 0.34
8. 9 × 7.21
9. 4 × 5.2
10. 7 × 17.2
11. 4 × 3.92
12. 8 × 0.21
13. Logan multiplies 5.31 by 3 and says the product is
159.3. Explain why Logan’s answer is not correct.
© Houghton Mifflin Harcourt Publishing Company
Problem
Problem Solving
Solving
14. Minnie rides her bike 2.76 miles each day.
How many miles will she bike in 7 days?
15. Dominick buys a package of soup mix that
is 1.38 ounces. How many ounces are
6 packages of soup mix?
Module 3 • Lesson 3 121
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
If she triples the recipe, how many ounces of
beans will Sandra need?
A
17.29 ounces
B
18.83 ounces
C
19.17 ounces
D
20.19 ounces
17. Kip uses the Distributive Property to rewrite
an expression.
(4 × 3) + (4 × 0.7)
What is the value of the expression?
A
3.07
B
11.7
C
14.8
D
29.6
18. Manny charges $1.25 for a cup of lemonade
19. Fabric costs $11.99 a yard. Leo buys 4 yards
at the lemonade stand. He sells 9 cups. How
much money does Manny collect?
of red fabric and 3 yards of blue fabric. How
much does Leo spend on fabric?
A
$10.75
A
$47.96
B
$11.00
B
$35.97
C
$11.25
C
$77.33
D
$11.75
D
$83.93
20. Multi-Step On the first day of summer, a
122
21. Multi-Step Nicky bought 14.2 pounds of
rainstorm brought 2.29 inches of rain to the
area. During the rest of the summer, there was
3 times as much rain as on the first day. What
was the total number of inches of rainfall for
the summer?
coffee for the coffee shop. The shop usually
uses 5 times that amount of coffee during one
week. How much more coffee will Nicky need
to purchase to get the right amount of coffee
for the week?
A
6.29 inches
A
71 pounds
B
5.67 inches
B
56.8 pounds
C
6.87 inches
C
85.2 pounds
D
9.16 inches
D
50 pounds
© Houghton Mifflin Harcourt Publishing Company
16. Sandra uses 6.39 ounces of beans in a recipe.