8

   

  mixed number A number
represented by a whole number and
a fraction

multiple A number that is the

Dear Family, product of a given number and a
counting number
During the next few weeks, our math class will be unit fraction A fraction that has
learning how to multiply fractions and mixed numbers 1 as its top number or numerator
by whole numbers. We will learn to write a fraction as
a product of a whole number and a unit fraction, and
to find multiples of unit fractions.
You can expect to see homework that provides
practice multiplying fractions and whole numbers
with and without using models.
Here is a sample of how your child will be taught
to use a number line to find multiples of a fraction.

Use a Number Line to Write Multiples of Fractions

Write 3 3 3
__ as the product of a whole number and a unit fraction.

4
Renaming as a Mixed
STEP 1 Number
Start at 0. Draw jumps to find multiples of 3
__: 3
__, 6
__, 9
__.
When the numerator
4 4 4 4
is greater than the
denominator, the fraction
can be renamed as a
' ( ) * + , - . / 0 ('
+ + + + + + + + + + mixed number.
9
__ 5 4
__ 1 4
__ 1 1
__
STEP 2
4 4 4 4
1
5 2 1 __
Write the multiple as a product of a whole number 4
52
1
__
© Houghton Mifflin Harcourt Publishing Company

and a unit fraction.

4
So, 3 3 3
__ 5 9
__ 5 9 3 1
__.
4 4 4

Activity
Use everyday situations, such as cooking and measures to help
your child practice fraction multiplication.

Chapter 8 P155
 8
 



fracción unitaria Una fracción que tiene

 al 1 como numerador, es decir, arriba de
la barra

múltiplo Un número que es el producto

de cierto número y un número positivo
Querida familia, distinto de cero

Durante las próximas semanas, en la clase de número mixto Un número que se

representa por un número entero y una
matemáticas aprenderemos a multiplicar fracciones fracción
y números mixtos por números enteros. También
aprenderemos a escribir fracciones como el producto
de un número entero y una fracción unitaria y a hallar
múltiplos de fracciones unitarias.
Llevaré a casa tareas para practicar la multiplicación
de fracciones y números enteros usando modelos y sin
modelos.
Este es un ejemplo de cómo vamos a usar una recta
numérica para hallar los múltiplos de una fracción.

Usar una recta numérica para escribir múltiplos de fracciones

Escribe 3 3 3_4 como el producto de un número entero y una


fracción unitaria. Expresarlo como un número
mixto
PASO 1
Cuando el numerador es
Comienza en 0. Dibuja saltos para hallar los múltiplos de 3
__: 3
__, 6
__, 9
__
4 4 4 4 mayor que el denominador,
la fracción se puede expresar
como un número mixto.

' ( ) * + , - . / 0 (' 954

__ __ 1 4
__ 1 1
__
+ + + + + + + + + + 4 4 4 4
1
5 2 1 __
4
PASO 2 52
1
__
4 © Houghton Mifflin Harcourt Publishing Company
Escribe el múltiplo como el producto de un número entero y una
fracción unitaria.

Actividad
Use situaciones de la vida diaria, como cocinar y medir para ayudar a su
hijo o hija a practicar la multiplicación con fracciones.

P156
 Lesson 8.1
Name
Multiples of Unit Fractions COMMON CORE STANDARD MACC.4.NF.2.4a

Build fractions from unit fractions by applying and

extending previous understandings of operations
on whole numbers.

Write the fraction as a product of a whole number and a unit fraction.

1
_
5
1. __ 5
53 7
2. __ 5
5
3. __ 5
6 ___ 6 8 ___ 3 ___

9
4. ___ 5
3
5. __ 5
11
6. ___ 5
10 ___ 4 ___ 12 ___

4
7. __ 5
8
8. ___ 5
13
9. ____ 5
6 ___ 20 ___ 100 ___

List the next four multiples of the unit fraction.

1
10. __,
1
11. __,
5 , , , 8 , , ,
© Houghton Mifflin Harcourt Publishing Company

12. So far, Monica has read _56 of a book. She 13. Nicholas buys _38 pound of cheese. He
has read the same number of pages each puts the same amount of cheese on
day for 5 days. What fraction of the book 3 sandwiches. How much cheese does
does Monica read each day? Nicholas put on each sandwich?

Chapter 8 P157
Lesson Check (MACC.4.NF.2.4a)
1. Selena walks from home to school each 2. Will uses _34 cup of olive oil to make
morning and back home each afternoon. 3 batches of salad dressing. How much
Altogether, she walks 2_3 mile each day. oil does Will use for one batch of salad
How far does Selena live from school? dressing?
A 1 mile
__ 1 cup
__
A
3 4
B 2__ mile
B 1__ cup
3 3
1 miles
C 1__ 1 cups
C 2__
3 4
D 2 miles D 3 cups

Spiral Review (MACC.4.OA.2.4, MACC.4.NF.1.1, MACC.4.NF.2.3b, MACC.4.NF.2.3d)

3. Liza bought 5_8 pound of trail mix. She 4. Leigh has a piece of rope that is 6 _23 feet
gives 1_ pound of trail mix to Michael.
8 long. How do you write 6 2_ as a fraction
3
How much trail mix does Liza have left? greater than 1? (Lesson 7.6)
(Lesson 7.5)
A 11
___
1 pound
A __
3
8 B 15
___
3
B 2
__ pound
8 C 20
___
3
C 3
__ pound
8 62
D ___
3
D 4
__ pound
8

5. Randy’s house number is a composite 6. Mindy buys 12 cupcakes. Nine of the

number. Which of the following could cupcakes have chocolate frosting and the
be Randy’s house number? (Lesson 5.5) rest have vanilla frosting. What fraction of © Houghton Mifflin Harcourt Publishing Company

A 29 the cupcakes have vanilla frosting?

(Lesson 6.3)
B 39 1
A __
C 59 4
D 79 B 1
__
3
C 2
__
3
D 3
__
4

P158
 Lesson 8.2
Name
Multiples of Fractions COMMON CORE STANDARD MACC.4.NF.2.4b

Build fractions from unit fractions by applying and

extending previous understandings of operations on
whole numbers.

List the next four multiples of the fraction.

3
1. __,
2
2. __,
5 , , , 6 , , ,

4
3. __,
5
4. ___,
8 , , , 10 , , ,

Write the product as the product of a whole number and a unit fraction.

5. 6.

' ( ) * + , - . / 0 (' ' ( ) * + , - . / 0 ('

, , , , , , , , , , * * * * * * * * * *

234
__ 5 532
__ 5
5 _ __ 3 _ __
© Houghton Mifflin Harcourt Publishing Company

7. Jessica is making 2 loaves of banana 8. A group of four students is performing an

bread. She needs _34 cup of sugar for experiment with salt. Each student must
each loaf. Her measuring cup can only add 3_8 teaspoon of salt to a solution. The
hold 1_4 cup of sugar. How many times will group only has a 1_8 -teaspoon measuring
Jessica need to fill the measuring cup in spoon. How many times will the group
order to get enough sugar for both loaves need to fill the measuring spoon in order
of bread? to perform the experiment?

Chapter 8 P159
Lesson Check (MACC.4.NF.2.4b)
1. Eloise made a list of some multiples of _58 . 2. David is filling five _34 -quart bottles with
Which of the following lists could be a sports drink. His measuring cup only
Eloise’s list? holds 1_4 quart. How many times will
5, ___
A __ 10, ___
15, 20
___, 25
___ David need to fill the measuring cup
8 16 24 32 40 in order to fill the 5 bottles?
B 5
__, 10
___, 15
___, 20
___, 25
___
A 5
8 8 8 8 8
5, __
C __ 6, __
7, __
8, 9
__ B 10
8 8 8 8 8
C 15
2, __
1, __
D __ 3, __
4, 5
__
8 8 8 8 8 D 20

Spiral Review (MACC.4.NBT.2.6, MACC.4.OA.1.3, MACC.4.NF.2.3c, MACC.4.NF.1.2)

3. Ira has 128 stamps in his stamp album. 4. Ryan is saving up for a bike that costs
He has the same number of stamps on $198. So far, he has saved $15 per week
each of the 8 pages. How many stamps for the last 12 weeks. How much more
are on each page? (Lesson 4.11) money does Ryan need in order to be
able to buy the bike? (Lesson 3.7)
A 12
A $8
B 14
B $18
C 16
C $48
D 18
D $180

5. Tina buys 3 _78 yards of material at the 6. Which list shows the fractions in order
fabric store. She uses it to make a skirt. from least to greatest? (Lesson 6.8)
Afterward, she has 1 3_8 yards of the fabric 2, __
A __ 3, ___
7
leftover. How many yards of material did 3 4 12
7,3 __, 2
© Houghton Mifflin Harcourt Publishing Company

Tina use? (Lesson 7.7) B ___ __

12 4 3
A 14
__ yards
3, __
2, ___
7
8 C __
4 3 12
B 21
__ yards
7 , __
2, __
3
8 D ___
12 3 4
C 24
__ yards
8
D 52
__ yards
8

P160
 Lesson 8.3
Name
Multiply a Fraction by a Whole COMMON CORE STANDARD MACC.4.NF.2.4b

Build fractions from unit fractions by applying and

Number Using Models extending previous understandings of operations on
whole numbers.

Multiply.
10
__
5
1. 2 3 __ 5
2
2. 3 3 __ 5
3
3. 7 3 ___ 5
6 _ 6
_ 5 __ 10 __

5
4. 3 3 ___ 5
3
5. 6 3 __ 5
2
6. 4 3 __ 5
12 __ 4 __ 8 __

2
7. 5 3 __ 5
7
8. 2 3 __ 5
4
9. 6 3 __ 5
3 __ 8 __ 5 __
© Houghton Mifflin Harcourt Publishing Company

10. Matthew walks _58 mile to the bus stop each 11. Emily uses _23 cup of milk to make one
morning. How far will he walk in 5 days? batch of muffins. How many cups of
milk will Emily use if she makes
3 batches of muffins?

Chapter 8 P161
Lesson Check (MACC.4.NF.2.4b)
1. Aleta’s puppy gained _38 pound each week 2. Pedro mixes _34 teaspoon of plant food
for 4 weeks. Altogether, how much weight into each gallon of water. How many
did the puppy gain during the 4 weeks? teaspoons of plant food should Pedro
8 pound
A ___ mix into 5 gallons of water?
12 3 teaspoon
A ___
B 12
__ pounds 20
8 4 teaspoon
B ___
C 12
___ pounds 15
8
C 8__ teaspoons
D 43
__ pounds 4
8
D 15
___ teaspoons
4

Spiral Review (MACC.4.NF.1.2, MACC.4.NF.2.3b, MACC.4.NF.2.3c, MACC.4.NF.2.4a)

3. Ivana has 3_4 pound of hamburger meat. 4. Which of the following expressions is
She makes 3 hamburger patties. Each NOT equal to __7
? (Lesson 7.2)
10
patty weighs the same amount. How 5 1 ___
A ___ 1 1 ___
1
much does each hamburger patty weigh? 10 10 10
(Lesson 8.1) 2 1 ___
B ___ 2 1 ___
3
10 10 10
A 1
__ pound
4 3 1 ___
C ___ 3 1 ___
2
1 10 10 10
B __ pound 4 1 ___
2 1 ___
1
3 D ___
10 10 10
C 21
__ pounds
4
D 3 pounds

5. Lance wants to find the total length 6. Which of the following statements is true?
of 3 boards. He uses the expression (Lesson 6.6)

( )
© Houghton Mifflin Harcourt Publishing Company

3 1_2 1 2 1 4 1_2 . How can Lance rewrite A 5 . ___

__ 9
the expression using both the Associative 8 10
and Commutative Properties of Addition? 5 .1
B ___ __
(Lesson 7.9)
12 3
3 . __
C __ 4
A 5 1 41
__
2
C 2 1 31(
__ 1 41
2
__ )
2 6 5
B (31__2 1 2) 1 41__2 D __ 1 (4__
31 1 1 2) D 1__ . 3
__
2 2 2 4

P162
 Lesson 8.4
Name
Multiply a Fraction or Mixed COMMON CORE STANDARD MACC.4.NF.2.4c

Build fractions from unit fractions by applying and

Number by a Whole Number extending previous understandings of operations on
whole numbers.

Multiply. Write the product as a mixed number.

5
1__
3 3
2. 3 3 __ 5 3. 5 3 __ 5
3
1. 5 3 ___ 5
10 _10
_ 5 __ 4 __

1
4. 4 3 1__ 5
1
5. 2 3 2__ 5 6. 5 3 1__ 5
1
5 __ 3 __ 6 __

7
7. 2 3 2__ 5
3
8. 7 3 1__ 5 9. 8 3 1__ 5
3
8 __ 4 __ 5 __
© Houghton Mifflin Harcourt Publishing Company

10. Brielle exercises for _34 hour each day for 11. A recipe for quinoa calls for 2 _23 cups of
6 days in a row. Altogether, how many milk. Conner wants to make 4 batches of
hours does she exercise during the 6 days? quinoa. How much milk does he need?

Chapter 8 P163
Lesson Check (MACC.4.NF.2.4c)
1. A mother is 1 _34 times as tall as her son. 2. The cheerleaders are making a banner
Her son is 3 feet tall. How tall is the that is 8 feet wide. The length of the
mother? banner is 1 1_3 times the width of the
3 feet
A 4 __
banner. How long is the banner?
4 A 81__ feet
1 feet 3
B 5 __
4 B 83 __ feet
1 feet
C 5 __
8
2 1 feet
C 10 __
3 feet 3
D 5 __
4 2 feet
D 10 __
3

Spiral Review (MACC.4.NF.2.3c, MACC.4.NF.2.4a, MACC.4.NF.2.4b)

3. Karleigh walks 5_8 mile to school every day. 4. Which number is a multiple of 4_5 ? (Lesson 8.2)
How far does she walk to school in 8
A ___
5 days? (Lesson 8.3) 10
5 mile
A ___ B 12
___
40 15
B 25
___ mile C 16
___
40 20
C 10
___ miles D 12
___
8 5
25
D ___ miles
8

5. Jo cut a key lime pie into 8 equal-size 6. Over the weekend, Ed spent 1 _14 hours
slices. The next day, _7 of the pie is left.
8 doing his math homework and 1 _3 hours
4
Jo puts each slice on its own plate. How doing his science project. Altogether, © Houghton Mifflin Harcourt Publishing Company

many plates does she need? (Lesson 8.1) how much time did Ed spend doing
A 5 homework over the weekend? (Lesson 7.7)
A 3 hours
B 6
3 hours
B 2__
C 7 4
D 8 1 hours
C 2__
2
D 2 hours

P164
 PROBLEM SOLVING
Name
Lesson 8.5
Problem Solving Ä Comparison
COMMON CORE STANDARD MACC.4.NF.2.4c
Problems with Fractions Build fractions from unit fractions by applying and
extending previous understandings of operations on
whole numbers.

Read each problem and solve.

1. A shrub is 1 _23 feet tall. A small tree is 3 times as

tall as the shrub. How tall is the tree?

t is the height of the tree, in feet.

shrub _
12
t 5 3 3 12_ 3
3
_
5 tree _
12 1_
2 _
12
t533 3 3 3
3
__
t 5 15
3
t55
So, the tree is 5 feet tall. ____ 5 feet
2. You run 1 _34 miles each day. Your friend runs
4 times as far as you do. How far does your
friend run each day?

____

3. At the grocery store, Ayla buys 1 _13 pounds of

ground turkey. Tasha buys 2 times as much
ground turkey as Ayla. How much ground
turkey does Tasha buy?

____
© Houghton Mifflin Harcourt Publishing Company

4. When Nathan’s mother drives him to school, it

takes _1 hour. When Nathan walks to school, it
5
takes him 4 times as long to get to school. How
long does it take Nathan to walk to school?

____

Chapter 8 P165
Lesson Check (MACC.4.NF.2.4c)
1. A Wilson’s Storm Petrel is a small bird 2. The walking distance from the Empire
with a wingspan of 1 1_ feet. A California
3 State Building in New York City to Times
Condor is a larger bird with a wingspan Square is about __9
10 mile. The walking
almost 7 times as wide as the wingspan distance from the Empire State Building
of the petrel. About how wide is the to Sue’s hotel is about 8 times as far.
wingspan of the California Condor? About how far is Sue’s hotel from the
4 foot
A ___ Empire State Building?
21 9 mile
___
A
B 21
__ feet 80
3
B 72
___ mile
C 71
__ feet 80
3 7 miles
C 1___
D 91
__ feet 10
3 2 miles
D 7___
10

Spiral Review (MACC.4.OA.2.4, MACC.4.NF.1.2, MACC.4.NF.2.3d, MACC.4.NF.2.4c)

3. Which of the following expressions is 4. At a bake sale, Ron sells _78 of an apple
NOT equal to 3 3 2 _1 ? (Lesson 8.4)
4 pie and _5 of a cherry pie. Altogether, how
8
A 339
__ much pie does he sell at the bake sale?
4 (Lesson 7.5)

B (3 3 2) 1 (3 3 __
1)
A 2
__
4 8
3
C 6 __ 12
4 B ___
16
D 33211 __
C 12
___
4 8
35
D ___
8
© Houghton Mifflin Harcourt Publishing Company

5. On a ruler, which measurement is 6. Which of the following numbers is

between __3
inch and 7_ inch?
16 8 composite? (Lesson 5.5)
(Lesson 6.8)
A 4 C 2
1 inch
A ___ 11 inch
C ___
16 16 B 3 D 1
B 1
__ inch D 15
___ inch
8 16

P166
 COMMON CORE STANDARDS MACC.4.NF.2.4a,
Name MACC.4.NF.2.4b, MACC.4.NF.2.4c

Chapter 8 Extra Practice

Lesson 8.1
Write the fraction as a product of a whole number and a
unit fraction.

5
1. __ 5
7
2. __ 5
3
3. __ 5
6 ___ 8 ___ 5 ___

List the next four multiples of the unit fraction.

1
4. __,
1
5. __,
2 , , , 6 , , ,

Lesson 8.2
List the next four multiples of the fraction.

3
1. ___,
7
2. ___,
10 , , , 12 , , ,

Write the product as the product of a whole number and a unit fraction.
© Houghton Mifflin Harcourt Publishing Company

3. 4.

' ( ) * + , - . / 0 (' ' ( ) * + , - . / 0 ('

- - - - - - - - - - / / / / / / / / / /

3
2 3 __ 5 ___ 332
__ 5
6 8 _ __

Chapter 8 P167
Lesson 8.3
Multiply.

7
1. 3 3 ___ 5
4
2. 5 3 __ 5
6
3. 4 3 ___ 5
10 __ 8 __ 12 __

3
4. 2 3 __ 5
3
5. 6 3 __ 5
2
6. 7 3 ___ 5
4 __ 5 __ 10 __

Lesson 8.4
Multiply. Write the product as a mixed number.

8
1. 4 3 ___ 5
5
2. 3 3 __ 5
1
3. 2 3 3 __ 5
10 __ 6 __ 3 __

4. 4 3 2 __ 5
2 7
5. 5 3 1__ 5
3
6. 3 3 3 __ 5
5 __ 8 __ 4 __

Lesson 8.5
1. A shrub in Pam’s back yard is about 2. A puppy weighs __
9
10 pound. Its mother
1 3_ feet tall. A small tree in her back yard
8 weighs 8 times as much. How much
is 7 times as tall as the shrub. About how does the mother weigh? © Houghton Mifflin Harcourt Publishing Company

tall is the tree?

P168