Lesson 8.
3
Name
Multiply a Fraction by a Whole Number Numbers and Operations—
Fractions—4.NF.B.4b Also 4.NF.B.4c
Using Models MATHEMATICAL PRACTICES
Essential Question How can you use a model to multiply a fraction MP1, MP2, MP4
by a whole number?
Unlock
Unlock the
the Problem
Problem
Rafael practices the violin for 3_4 hour each day. He has a
recital in 3 days. How much time will he practice in 3 days? • How many equal groups
of 3_4 should you model?
Example 1 Use a model to multiply 3 × 3_4.
Think: 3 × 3_4 is 3 groups of 3_4 of a whole. Shade the model to
show 3 groups of 3_4 .
1 group of 3
__ =
4 _
2 groups of 3
__ =
4 _
3 groups of 3
__ =
Math
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (r) ©TongRo Image Stock/Alamy Images
4 _
MATHEMATICAL PRACTICES 2
Talk
3×3 __ =
4 _ Reason Abstractly If you
multiply 4 × 2_6 , is the
So, Rafael will practice for _ hours in all. product greater than or
less than 4? Explain.
1. Explain how you can use repeated addition with the
model to find the product 3 × 3_4 .
2. Rafael’s daily practice of 3_4 hour is in sessions that
last for 1_4 hour each. Describe how the model shows
the number of practice sessions Rafael has in 3 days.
Chapter 8 469
Example 2 Use a pattern to multiply.
You know how to use a model and repeated addition to multiply
a fraction by a whole number. Look for a pattern in the table to
discover another way to multiply a fraction by a whole number.
Whole Number Fraction
Multiplication Problem Product
(Number of Groups) (Size of Groups)
1 1 1 1 1 1
6 6 6 6 6 6 1 2
2 × 1_ 2 _ of a whole _
1 1 1 1 1 1 6 6 6
6 6 6 6 6 6
1 1 1 1 1 1
6 6 6 6 6 6 2 4
2 × 2_ 2 _
6
of a whole _
6
1 1 1 1 1 1 6
6 6 6 6 6 6
1 1 1 1 1 1
6 6 6 6 6 6 3_ 6_
2 × 3_ 2 of a whole
1 1 1 1 1 1 6 6 6
6 6 6 6 6 6
When you multiply a fraction by a whole number, the numerator
in the product is the product of the ___ and the
___ of the fraction. The denominator in the product
is the same as the ___ of the fraction.
3. How do you multiply a fraction by a whole number without using
a model or repeated addition?
© Houghton Mifflin Harcourt Publishing Company
4. Describe two different ways to find the product 4 × 2_3 .
470
Name
MATH
M
Share
Share and
and Show
hhow
Sh BOARD
B
1. Find the product of 3 × 5_.
8
1 group of _5 = _____
8 8
2 groups of _5 = _____
8 8
3 groups of 5_ = _____ 5
8 8 3 groups of
8
3 × 5_ = _
8
Multiply.
2. 3. 1 1 1
1 1 1 1 3 3 3
5 5 5 5
1 1 1
1 1 1 1 3 3 3
5 5 5 5
1 1 1 1 1
5 5 3 3 3
1 1 1
3 3 3
2 × 4_ = 4 × 2_ =
5 _ 3 _
3
4. 5 × __ = 5. 4 × 5_ = Math MATHEMATICAL PRACTICES 4
10 _ 6 _ Talk
Model Mathematics
Describe how to model
Exercise 5.
On
On Your
Your Own
Own
Multiply.
© Houghton Mifflin Harcourt Publishing Company
7
6. 2 × __ = 7. 6 × 3_ = 8. 5 × 2_ =
12 _ 8 _ 4 _
9. 3 × 4_ = 5
10. 2 × __ = 11. 4 × 2_ =
6 _ 10 _ 8 _
MATHEMATICAL
PRACTICE 7 Look for a Pattern Algebra Write the unknown number.
7
14. 2 × ____ = 14
__
12. × 2_ = 12
__ 13. 5 × ____ = 10
__
8
3 3 4 4
Chapter 8 • Lesson 3 471
MATHEMATICAL PRACTICES COMMUNICA5&t1&34E7&3&tCONSTRUCT ARGUMENTS
Unlock
Unlock the
the Problem
Problem
15. Lisa makes clothes for pets.
_5
She needs yard of fabric to make 1 dog coat.
6
How much fabric does she need to make
3 dog coats?
a. What do you need to find?
b. What information do you need?
c. Show the steps you use to solve the problem.
WRITE M t Show Your Work
Math
d. Complete the sentence.
Lisa needs _ yards of fabric to make 3 dog coats.
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) ©Petra Wegner/Alamy Images
16. DEEPER Manuel’s small dog eats 2_4 bag of 17. SMARTER
Select the correct product
dog food in 1 month. His large dog eats for the equation.
3_ bag of dog food in 1 month. How many
4
bags do both dogs eat in 6 months?
24 18 24 18
12 12 7 7
2
9 × __ = 3 × 6_ =
12 7
6 × 4_ = 3
8 × __ =
7 12
472
Practice and Homework
Name
Lesson 8.3
Multiply a Fraction by a Whole Number
Using Models COMMON CORE STANDARD—4.NF.B.4
Build fractions from unit fractions by applying
and extending previous understandings of
operations on whole numbers..
Multiply.
10
__
1. 2 × 5
__ =
6 2. 3 × 2
__ = 3 =
3. 7 × ___
6 __ 5 __ 10 __
5 =
4. 3 × ___ 5. 6 × 3
__ = 6. 4 × 2
__ =
12 __ 4 __ 5 __
Problem
Problem Solving
Solving
7. Matthew walks 5_8 mile to the bus stop each 8. Emily uses 2_3 cup of milk to make one batch
morning. How far will he walk in 5 days? of muffins. How many cups of milk will Emily
use if she makes 3 batches of muffins?
© Houghton Mifflin Harcourt Publishing Company
9. WRITE Math Explain how you can use a model to find
4 × 3_8 . Include a drawing and a solution.
Chapter 8 473
Lesson Check (4.NF.B.4b)
1. Aleta’s puppy gained 3_8 pound each week for 2. Pedro mixes __
3 teaspoon of plant food into
4
4 weeks. Altogether, how much weight did each gallon of water. How many teaspoons
the puppy gain during the 4 weeks? of plant food should Pedro mix into
5 gallons of water?
Spiral Review (4.NF.A.2, 4.NF.B.3b, 4.NF.B.3c, 4.NF.B.4a)
3. Ivana has _34 pound of hamburger meat. __
7 as a sum of fractions two different
4. Write 10
She makes 3 hamburger patties. Each patty ways.
weighs the same amount. How much does
each hamburger patty weigh?
5. Lance wants to find the total length of 3 boards. 6. Fill in the blank with a symbol that makes
He uses the expression 3 _12 + (2 + 4 1_2 ). How this statement true:
can Lance rewrite the expression using
both the Associative and Commutative
© Houghton Mifflin Harcourt Publishing Company
Properties of Addition?
5
___ 1__
12 3
FOR MORE PRACTICE
GO TO THE
474 Personal Math Trainer
