School-Home

7
Chapter

Letter denominator The part of the fraction

below the line, which tells how many
equal parts there are in the whole or in
a group

Dear Family, mixed number A number represented

by a whole number and a fraction
Throughout the next few weeks, our math class will be numerator The part of a fraction
learning about multiplying fractions and mixed numbers. above the line, which tells how many
We will also be using area models to help understand parts are being counted

fraction multiplication. product The answer in a

multiplication problem
You can expect to see homework with real-world
simplest form A fraction in which
problems that involve multiplication with fractions and 1 is the only number that can divide
mixed numbers. evenly into the numerator and the
denominator
Here is a sample of how your child is taught to multiply
two mixed numbers.

Multiply Mixed Numbers Tips

Multipy. 1 3_4 × 2 1_2 Checking for Reasonable
Answers Tips
STEP 1
When a fraction is multiplied
Write the mixed numbers as fractions. by 1, the product equals the
13__4 × 21__ = 7__ × 5__ fraction. When a fraction is
2 4 2
STEP 2 multiplied by a factor greater
than 1, the product will be
Multiply the fractions.
×5 greater than the fraction. When
= 7_____
STEP 3 4×2 a fraction is multiplied by a
factor less than 1, the product
= 35
___
Write the product as a mixed number in 8 will be less than either factor.
simplest form. = 43__
8

Activity
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Use recipes to practice multiplication with fractions and mixed numbers. Work
together to solve problems such as, “One batch of the recipe calls for 2 1_4 cups of
flour. How much flour would we need to make 1 1_2 batches?”

Chapter 7 P133
 7 Carta
Capítulo

denominador La parte de la fracción

para la casa debajo de la barra que indica cuántas
partes iguales hay en un total o en un grupo

número mixto Un número representado

por un número entero y una fracción
Querida familia,
numerador La parte de una fracción por
Durante las próximas semanas, en la clase de matemáticas encima de la barra que indica cuántas
aprenderemos a multiplicar fracciones y números mixtos. partes se están contando

También aprenderemos a usar modelos de área para producto El resultado de un problema de

multiplicación
entender la multiplicación de fracciones.
mínima expresión Una fracción en la que
Llevaré a la casa tareas con problemas del mundo real que 1 es el único número que se puede dividir
involucren la multiplicación con fracciones y números mixtos. en partes iguales entre el numerador y el
denominador
Este es un ejemplo de la manera como aprenderemos a
multiplicar dos números mixtos.

Multiplicar números mixtos

Multiplica. 1 3_4 × 2 1_2 Pistas

Buscar respuestas razonables
PASO 1
Cuando una fracción se multiplica
Escribe los números mixtos como fracciones.
por 1, el producto es igual a la
1__34 × 21__ = 7__ × 5__
2 4 2 fracción. Cuando una fracción se
PASO 2 multiplica por un factor mayor que
Multiplica las fracciones. 1, el producto será mayor que la
7×5
= _____ fracción. Cuando una fracción
4×2 se multiplica por un factor menor
PASO 3
que 1, el producto será menor que
= 35
___
Escribe el producto como un número mixto 8 ese factor.
en su mínima expresión. = 4__3
8

Actividad © Houghton Mifflin Harcourt Publishing Company

Usen recetas para practicar la multiplicación con fracciones y números mixtos.

Trabajen juntos para resolver problemas como, “Una porción de la receta pide 2 1_4
tazas de harina. ¿Cuánta harina necesitaremos para hacer 1 1_2 porciones?”

P134
 Lesson 7.1
Name
Find Part of a Group COMMON CORE STANDARD—5.NF.4a
Apply and extend previous understandings
of multiplication and division to multiply and
divide fractions.

Use a model to solve.

9
1. __34 × 12 = _ 2. __78 × 16 = _

6
3. __
10 × 10 = _ 4. __23 × 9 = _

5. __16 × 18 = _ 6. __45 × 10 = _

Problem
Problem Solving
Solving
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7. Marco drew 20 pictures. He drew 3_4 of them in 8. Caroline has 10 marbles. One half of them
art class. How many pictures did Marco draw in are blue. How many of Caroline’s marbles
art class? are blue?

Chapter 7 P135
Lesson Check (5.NF.4a)
1. Use the model to find 1_3 × 15. 2. Use the model to find 2_4 × 16.

Spiral Review (5.NBT.1, 5.NBT.6, 5.NF.1, 5.NF.2)

3. What is the value of the underlined digit? 4. Nigel has 138 fluid ounces of lemonade. How
many 6-fluid-ounce servings of lemonade can
he make?

6,560

5. Rafi had a board that was 15 1_2 feet long. 6. Susie spent 4 1_4 hours on Monday and 3 5_8 hours
He cut three pieces off the board that are each on Tuesday working on a history project. About © Houghton Mifflin Harcourt Publishing Company
3 7_8 feet long. How much of the board is left? how long did she spend working on the project?

P136
 Lesson 7.2
Name
Multiply Fractions and Whole Numbers COMMON CORE STANDARD—5.NF.4a
Apply and extend previous understandings
of multiplication and division to multiply
and divide fractions.
Use the model to find the product.

5
_ 1
12 × 3 =
1. __
5 , or 1_ 2. 3 × __34 =
4
___ 4 ___

1 1 1
1 1 1 1 1 1 1 1 1 1 1 1
4 4 4 4 4 4 4 4 4 4 4 4

Find the product.

3. __25 × 5 = ___ 4. 7 × __23 = 5. __38 × 4 =

___ ___

6. 7 × __56 = 7. __
5
12 × 6 = 8. 9 × __23 = ___
___ ___

Problem
Problem Solving
Solving
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9. Jody has a 5-pound bag of potatoes. She uses 4_5 of 10. Lucas lives 5_8 mile from school. Kenny lives twice
the bag to make potato salad. How many pounds as far as Lucas from school. How many miles
of potatoes does Jody use for the potato salad? does Kenny live from school?

Chapter 7 P137
Lesson Check (5.NF.4a)
1. In gym class, Ted runs 4_5 mile. His teacher runs 2. Jon is decorating a banner for a parade. Jon uses
6 times that distance each day. How many miles a piece of red ribbon, which is 3_4 yard long. Jon
does Ted’s teacher run each day? also needs blue ribbon that is 5 times as long as
the red ribbon. How much blue ribbon does
Jon need?

Spiral Review (5.OA.1, 5.NBT.3b, 5.NF.2, 5.NF.3)

3. Mirror Lake Elementary School has 4. From an 8-foot board, a carpenter sawed off
168 students and chaperones going on one piece that was 2 3_4 feet long and another
the fifth grade class trip. Each bus can hold piece that was 3 1_2 feet long. How much of the
54 people. What is the least number of board was left?
buses needed for the trip?

5. What is the value of the expression? 6. Which of the following decimals has the least
value? 0.3; 0.029; 0.003; 0.01
30 − 5 × 4 + 2 © Houghton Mifflin Harcourt Publishing Company

P138
 Lesson 7.3
Name
Fraction and Whole Number Multiplication COMMON CORE STANDARD—5.NF.4a
Apply and extend previous understandings
of multiplication and division to multiply
and divide fractions.
Find the product. Write the product in simplest form.

1
2_
1. 4 × __58 = ____ 2 2. __29 × 3 = ____ 3. __45 × 10 = ____

4×_
5
= __
20
8 8
__
20
= 2_
4
, or 2 1_2
8 8

4. __34 × 9 = ____ 5. 8 × __56 = ____ 6. 7 × __12 = ____

3
7. __25 × 6 = ____ 8. 9 × __23 = ____ 9. __
10 × 9 = ____

10. 4 × __38 = ____ 11. __35 × 7 = ____ 12. __18 × 6 = ____

Problem
Problem Solving
Solving
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13. Leah makes aprons to sell at a craft fair. She 14. The gas tank of Mr. Tanaka’s car holds
needs 3_4 yard of material to make each apron. 15 gallons of gas. He used 2_3 of a tank of
How much material does Leah need to make gas last week. How many gallons of gas
6 aprons? did Mr. Tanaka use?

Chapter 7 P139
Lesson Check (5.NF.4a)
1. At the movies, Liz eats 1_4 of a box of popcorn. 2. It takes Ed 45 minutes to complete his science
Her friend Kyra eats two times as much popcorn homework. It takes him 2_3 as long to complete
as Liz eats. How much of a box of popcorn does his math homework. How long does it take Ed to
Kyra eat? complete his math homework?

Spiral Review (5.NBT.2, 5.NBT.7, 5.NF.1, 5.NF.2)

3. What is the best estimate for the quotient? 4. Sandy bought 3_4 yard of red ribbon and 2_3 yard
of white ribbon to make some hair bows.
591.3 ÷ 29
Altogether, how many yards of ribbon did
she buy?

5. Eric jogged 3 1_4 miles on Monday, 5 5_8 miles on 6. Sharon bought 25 pounds of ground beef and
Tuesday, and 8 miles on Wednesday. Suppose made 100 hamburger patties of equal weight.
he continues the pattern for the remainder of What is the weight of each hamburger patty?
the week. How far will Eric jog on Friday? © Houghton Mifflin Harcourt Publishing Company

P140
 Lesson 7.4
Name
Multiply Fractions COMMON CORE STANDARD—5.NF.4b
Apply and extend previous understandings of
multiplication and division to multiply and
divide fractions.
Find the product.
1. 2.

2 , or _
__ 1
1 2 2 5
__ __
12
4 × 3 = __ 6 __ __
5 × 6 = __

Find the product. Draw a model.

3. __45 × __12 = __ 4. __34 × __13 = __

5. __38 × __23 = __ 6. __35 × __35 = __

Problem
Problem Solving
Solving
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7. Nora has a piece of ribbon that is 3_4 yard long. She 8. Marlon bought 7_8 pound of turkey at the deli.
will use 1_2 of it to make a bow. What length of the He used 2_3 of it to make sandwiches for lunch.
ribbon will she use for the bow? How much of the turkey did Marlon use
for sandwiches?

Chapter 7 P141
Lesson Check (5.NF.4b)
1. Tina has 3_5 pound of rice. She will use 2_3 of it to 2. The Waterfall Trail is 3_4 mile long. At 1_6 of
make fried rice for her family. How much rice the distance from the trailhead, there is a
will Tina use to make fried rice? lookout. In miles, how far is the lookout
from the trailhead?

Spiral Review (5.OA.1, 5.NF.1, 5.NF.2, 5.NF.4a)

3. Hayden bought 48 new trading cards. Three- 4. Yesterday, Annie walked __ 9
10 mile to her friend’s
fourths of the new cards are baseball cards. house. Together, they walked 1_3 mile to the
How many baseball cards did Hayden buy? library. Which is the best estimate for how far
Annie walked yesterday?

5. Erin is going to sew a jacket and a skirt. She 6. Simplify the following expression.
needs 2 3_4 yards of material for the jacket and
1 1_2 yards of material for the skirt. Altogether, [(3 × 6) + (5 × 2)] ÷ 7
how many yards of material does Erin need?
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P142
 Lesson 7.5
Name
Compare Fraction Factors and Products COMMON CORE STANDARDS—5.NF.5a,
5.NF.5b Apply and extend previous
understandings of multiplication and division
to multiply and divide fractions.

Complete the statement with equal to, greater than, or less than.
less than
1. 3_5 × 4_7 will be ____ 4_7 . 2. 5 × 7_8 will be ____ 7_8 .

Think: 4_7 is multiplied by a

number less than 1;
so, 3_5 × 4_7 will be less than 4_7 .

3. 6 × 2_5 will be ____ 2_5 . 4. 1_9 × 1 will be ____ 1_9 .

5. 7_8 × 3_5 will be ____ 3_5 . 6. 4_5 × 7_7 will be ____ 4_5 .

Problem
Problem Solving
Solving
7. Starla is making hot cocoa. She plans to multiply 8. Miles is planning to spend 2_3 as many hours
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the recipe by 4 to make enough hot cocoa for bicycling this week as he did last week. Is Miles
the whole class. If the recipe calls for 1_2 teaspoon going to spend more hours or fewer hours
vanilla extract, will she need more than 1_2 bicycling this week than last week?
teaspoon or less than 1_2 teaspoon of vanilla
extract to make all the hot cocoa?

Chapter 7 P143
Lesson Check (5.NF.5a, 5.NF.5b)
1. Trevor saves 2_3 of the money he earns at his 2. Suppose you multiply a whole number greater
after-school job. Suppose Trevor starts saving 1_4 than 1 by the fraction 3_5 . Will the product be
as much as he is saving now. Will he be saving greater than, less than, or equal to 3_5 ?
less, more, or the same amount?

Spiral Review (5.NBT.6, 5.NBT.7, 5.NF.1)

3. In the next 10 months, Colin wants to save $900 4. What is the total cost of 0.5 pound of peaches
for his vacation. He plans to save $75 each of selling for $0.80 per pound and 0.7 pound of
the first 8 months. How much must he save oranges selling for $0.90 per pound?
each of the last 2 months in order to meet his
goal if he saves the same amount each month?

5. Megan hiked 15.12 miles in 6.3 hours. If Megan 6. It is 42 1_2 miles from Eaton to Baxter, and
hiked the same number of miles each hour, how 37 4_5 miles from Baxter to Wellington. How far
many miles did she hike each hour? is it from Eaton to Wellington, if you go by way
of Baxter?
© Houghton Mifflin Harcourt Publishing Company

P144
 Lesson 7.6
Name
Fraction Multiplication COMMON CORE STANDARD—5NF.4a
Apply and extend previous understandings
of multiplication and division to multiply
and divide fractions.
Find the product. Write the product in simplest form.

7 4
1. 4_ × _8 =
×7
___ 2. 3 × 1_6 3. _59 × 3_4 4. _47 × 1_ 5. _18 × 20
5 5 ×8 2

= __
28
40

= _7 __ __ __ __
10

6. _45 × 3_ 7. _67 × 7_ 8. 8 × 1_ 1 × 28
9. __
14
10. 3_4 × 1_3
8 9 9

__ __ __ __ __

11. Karen raked 3_5 of the yard. Minni raked 1_3 of the 12. In the pet show, 3_8 of the pets are dogs. Of the
amount Karen raked. How much of the yard did dogs, 2_3 have long hair. What fraction of the pets
Minni rake? are dogs with long hair?

Algebra Evaluate for the given value of the variable.

3 8 3
13. _78 × c for c = 8 14. t × _4 for t = _9 15. _12 × s for s = __
10 16. y × 6 for y = 2_3

__ __ __ __
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Problem
Problem Solving
Solving

17. Jason ran 5_7 of the distance around the school 18. A group of students attend a math club. Half
track. Sara ran 4_5 of Jason’s distance. What of the students are boys and 4_9 of the boys have
fraction of the total distance around the track brown eyes. What fraction of the group are boys
did Sara run? with brown eyes?

Chapter 7 P145
Lesson Check (5.NF.4a)
1. Fritz attended band practice for 5_6 hour. Then 2. Darlene read 5_8 of a 56-page book. How many
he went home and practiced for 2_5 as long as pages did Darlene read?
band practice. How many minutes did he
practice at home?

Spiral Review (5.NBT.2, 5.NF.1, 5.NF.3, 5.NF.4a)

3. What is the quotient of ____
18
1,000 ? 4. A machine produces 1,000 bowling pins per
hour, each valued at $8.37. What is the total
value of the pins produced in 1 hour?

5. Keith had 81_ cups of flour. He used 52_ cups to 6. The Blue Lake Trail is 11 3_8 miles long. Gemma
2 3
make bread. How many cups of flour does Keith has hiked 2 1_2 miles each hour for 3 hours. How
have left? far is she from the end of the trail?
© Houghton Mifflin Harcourt Publishing Company

P146
 Lesson 7.7
Name
Area and Mixed Numbers COMMON CORE STANDARD—5.NF.4b
Apply and extend previous understandings
of multiplication and division to multiply
and divide fractions.
Use the grid to find the area.
1. Let each square represent 1_4 unit by 1_4 unit. 2. Let each square represent 1_3 unit by 1_3 unit.
3 3_
2__14 × 1__12 = _8 1__23 × 2__13 = _

54 squares cover the diagram.

_
_161
Each square is _ square unit.

The area of the diagram is

54 × _1 = 54
_ = 3_3
16
____16 8 square units. The area is _ square units.

Use an area model to solve.

3. 11_ × 21_ 4. 22_ × 11_ 5. 13_4 × 21_

8 2 3 3 2

____ ____ ____

© Houghton Mifflin Harcourt Publishing Company

Problem
Problem Solving
Solving

6. Ava’s bedroom rug is 2 3_4 feet long and 2 1_2 feet 7. A painting is 2 2_3 feet long and 1 1_2 feet high. What is
wide. What is the area of the rug? the area of the painting?

Chapter 7 P147
Lesson Check (5.NF.4b)
1. The base of a fountain is rectangular. Its 2. Bill’s living room floor is covered with carpet
dimensions are 1 2_3 feet by 2 2_3 feet. What is the tiles. Each tile is 1 1_2 feet long by 2 3_5 feet wide.
area of the base of the fountain? What is the area of one tile?

Spiral Review (5.OA.2, 5.NBT.5, 5.NBT.6, 5.NF.4a)

3. Lucy earned $18 babysitting on Friday and $20 4. A grocery store clerk is putting cans of soup
babysitting on Saturday. On Sunday, she spent on the shelves. She has 12 boxes, which each
half of the money. Write an expression to match contain 24 cans of soup. Altogether, how many
the words. cans of soup will the clerk put on the shelves?

5. What is the best estimate for the quotient 6. There are 45 vehicles in a parking lot. Three
5,397 ÷ 62? fifths of the vehicles are minivans. How many of
the vehicles in the parking lot are minivans?

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P148
 Lesson 7.8
Name
Compare Mixed Number Factors and Products COMMON CORE STANDARDS—5.NF.5a,
5.NF.5b Apply and extend previous
understandings of multiplication and division to
multiply and divide fractions.
Complete the statement with equal to, greater than, or less than.

less than
1. 2_3 × 1 5_8 will be ____ 1 5_8 . 2. 5_5 × 2 3_4 will be ____ 2 3_4 .

Think: 1 × 1 5_8 is 1 5_8 .

Since 2_3 is less than 1,
_ × 1 5_ will be less than 1 5_ .
2
3 8 8

3. 3 × 3 2_7 will be ____ 3 2_7 . 4. 9 × 1 4_5 will be ____ 1 4_5 .

5. 1 7_8 × 2 3_8 will be ____ 2 3_8 . 6. 3 4_9 × 5_9 will be ____ 3 4_9 .

Problem
Problem Solving
Solving
7. Fraser is making a scale drawing of a dog house. 8. Jorge has a recipe that calls for 2 1_3 cups of flour.
© Houghton Mifflin Harcourt Publishing Company

The dimensions of the drawing will be 1_8 of the He plans to make 1 1_2 times the recipe. Will the
dimensions of the actual doghouse. The height amount of flour Jorge needs be equal to, greater
of the actual doghouse is 36 3_4 inches. Will the than, or less than the amount of flour his recipe
dimensions of Fraser’s drawing be equal to, calls for?
greater than, or less than the dimensions of the
actual dog house?

Chapter 7 P149
Lesson Check (5.NF.5a, 5.NF.5b)
1. Jenna skis 2 1_3 miles down the mountain. Her 2. Suppose you multiply a fraction less than 1 by
instructor skis 1 1_2 times as far. Does Jenna ski the mixed number 2 3_4 . Will the product be less
a shorter, greater, or the same distance as her than, greater than, or equal to 2 3_4 ?
instructor?

Spiral Review (NBT.2, 5.NBT.7, 5.NF.1)

3. Rectangular Washington County measures 4. Marsha jogged 7.8 miles. Erica jogged
15.9 miles by 9.1 miles. What is the county’s 0.5 times as far. How far did Erica jog?
area?

5. One bread recipe calls for 2 1_3 cups of flour. 6. On Monday, it rained 1 1_4 inches. On Tuesday,
Another bread recipe calls for 2 1_2 cups of flour. it rained 3_5 inch. How much more did it rain on
Tim has 5 cups of flour. If he makes both Monday than on Tuesday?
© Houghton Mifflin Harcourt Publishing Company

recipes, how much flour will he have left over?

P150
 Lesson 7.9
Name
Multiply Mixed Numbers COMMON CORE STANDARD—5.NF.6
Apply and extend previous understandings
of multiplication and division to multiply
and divide fractions.
Find the product. Write the product in simplest form.
3
1. 12_ × 42_ 2. 11_7 × 13_4 3. 81_ × _5 4. 25_ × 12_
3 5 3 8 3
_ _ _ _
12 3 42 5 5 3 22
3 5 3 5
5 __ _
110
5 22
15 3
57 _ 1
3
__ __ __

5. 51_ × 31_ 6. 71_ × 21_ 7. _23 × 41_ 8. 22_ × 11_4

2 3 5 6 5 5

__ __ __ __

Use the Distributive Property to find the product.

9. 42_ × 10 10. 26 × 21_ 11. 6 × 32_

5 2 3

__ __ __

Problem
Problem Solving
Solving
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12. Jake can carry 6 1_4 pounds of wood in from the 13. A glass can hold 331_ cups of water. A bowl can
barn. His father can carry 1 5_7 times as much as hold 2 3_5 times the amount in the glass. How many
Jake. How many pounds can Jake’s father carry? cups can a bowl hold?

_______ _______

Chapter 7 P151
Lesson Check (5.NF.6)
1. A vet weighs two puppies. The small puppy 2. Becky lives 5 5_8 miles from school. Steve lives
weighs 4 1_2 pounds. The large puppy weighs 1 5_9 times as far from school as Becky. How far
4 2_3 times as much as the small puppy. How does Steve live from school?
much does the large puppy weigh?

Spiral Review (5.OA.2, 5.NBT.6, 5.NF.1, 5.NF.2)

3. Craig scored 12 points in a game. Marla scored 4. Yvette earned $66.00 for 8 hours of work.
twice as many points as Craig but 5 fewer points Lizbeth earned $68.80 working the same
than Nelson scored. Write an expression to amount of time. How much more per hour
represent how many points Nelson scored. did Lizbeth earn than Yvette?

5. What is the least common denominator of the 6. Three girls collected geodes in the desert.
four fractions listed below? Corinne collected 11 1_8 pounds, Ellen collected
7 4 5_8 pounds, and Leonda collected 3 3_4 pounds.
20__ 203_4 9
18__ 2018
__
10 10 25 How much more did Corinne collect than the
other two girls combined?
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P152
 PROBLEM SOLVING
Name
Lesson 7.10
Problem Solving • Find Unknown Lengths
COMMON CORE STANDARD—5.NF.5b
Apply and extend previous understandings of
multiplication and division to multiply and
divide fractions.

1. Kamal’s bedroom has an area of 120 square feet. The Guess: 6 × 20 = 120
width of the room is __56 the length of the room. What are Check: 5_6 × 20 = 16 2_3 ; try a longer width.
the dimensions of Kamal’s bedroom?
Guess: 10 × 12 = 120
Check: 5_6 × 12 = 10. Correct!

10 feet by 12 feet
________

2. Marisol is painting on a piece of canvas that has an

area of 180 square inches. The length of the painting
is 1 1_4 times the width. What are the dimensions of
the painting?

________

3. A small plane is flying a banner in the shape of a

rectangle. The area of the banner is 144 square feet.
The width of the banner is 1_4 the length of the banner.
What are the dimensions of the banner?

________

4. An artificial lake is in the shape of a rectangle

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and has an area of __ 9 square mile. The width of

20
the lake is 1_5 the length of the lake. What are the
dimensions of the lake?

________

Chapter 7 P153
Lesson Check (5.NF.5b)
1. Consuelo’s living room is in the shape of a 2. A rectangular park has an area of 2_3 square mile.
rectangle and has an area of 360 square feet. The length of the park is 2 2_3 the width of the
The width of the living room is 5_8 its length. park. What is the width of the park?
What is the length of the living room?

Spiral Review (5.NBT.4, 5.NF.1, 5.NF.4a, 5.NF.5a, 5.NF.5b)

3. Debra babysits for 3 1_2 hours on Friday and 4. Tory practiced her basketball shots for 2_3 hour.
1 1_2 times as long on Saturday. Did Debra Tim practiced his basketball shots for 3_4 as
babysit more, fewer, or the same number of much time as Tory did. How long did Tim
hours on Saturday than she did on Friday? practice his basketball shots?

5. Leah bought 4 1_2 pounds of grapes. Of the grapes 6. To which place value is the following number
she bought, 1 7_8 pounds were red grapes. The rest rounded?
were green grapes. How many pounds of green
© Houghton Mifflin Harcourt Publishing Company

5.927 to 5.93
grapes did Leah buy?

P154