topic 10 - mrs. stephanie evans class websitemr. romano walks 1 __7 10 miles from his home to the...

Topic 10 Adding and

Subtracting Mixed numbers

_________ Name

___________ Test Date

Name

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5

Topic 10

Vocabulary Cards

Fold

her

e

proper fraction

mixed number

improper fraction

proper fraction

A fraction less than 1; its numerator is less than its

denominator.

mixed number

A number that combines a whole number and a

fraction

improper fraction

A fraction in which the numerator is greater than or equal to its

denominator

1 of 1Topic 10

Name


Name Daily Common Core Review10-1

1. �A�store�places�out-of-season�clothes�on�sale.�The�sales�price�is��1�_�3��of�the�original�price.�Which�expression�describes�the�new�sales�price?

A x�2��1�_�3��

B x�1��1�_�3��

C x�4��1�_�3��

D ��1�_�3��x

2. �Shelley�read�10�pages�of�a�book�on�Monday.�On�Tuesday,�she�read�twice�as�many�pages�as�she�read�on�Monday.�On�Wednesday,�she�read�twice�as�many�pages�as�she�read�on�Tuesday.�How�many�pages�did�she�read�in�all?�

A � 30�pages

B � 60�pages

C � 70�pages

D 100�pages

3. �Cara�lives��7�__�10��mi�from�school.�One�morning,�she�walks��1�_�5��mi�towards�school�and�meets�her�friend,�Aaron.�How�many�miles�from�school�are�they?

A ��6�_�5��mi

B ��1�_�2��mi

C ��3�_�5��mi

D ��8�__�15��mi

4. �Find��1�_�8��1��3�_�8��.�Simplify�your�answer�if�possible.�

5. What�is�the�measure�of�/A?�

6. �Draw�a�number�line�from�0�to�2.�Write��3�_�8��,1��3�_�4��and�1.25�on�the�number�line.

7. �Write�the�rule�for�the�table�as�an�algebraic�expression.�

In x 2 3 4 5

Out y 5 7 9 11

40°

A

B C

D 7•1D 10•1

Name


Practice

10-1Estimating Sums and Differences of Mixed NumbersRound to the nearest whole number.

1. 3 3 _ 8 2. 6 5 __ 11 3. 1 11 __ 20 4. 12 6 __ 13

Estimate each sum or difference.

5. 3 1 _ 4 + 2 5 _ 6 6. 5 6 _ 9 − 1 3 _ 4

7. 5 5 __ 13 + 8 3 _ 5 8. 11 − 6 3 _ 7 + 2 2 _ 5

Robert and May are competing in a track meet. The table at the right shows the results of their events.

9. Robert says his better jump was about 1 ft longer than May’s better jump. Is he correct?

10. Use the table above. If the school record for the softball throw is 78 ft, about how much farther must Robert throw the ball to match the record?

A 15 ft B 16 ft C 18 ft D 20 ft

11. Consider the sum of 3 _ 5 + 3 _ 4 . Round each fraction and estimate the sum. Add the two fractions using a common denominator and then round the result. Which estimate is closer to the actual answer?

Participant

Robert

May

Event Results/Distance

Long jump

Softball throw

Long jump

Softball throw

1. 6 5 __ 12 ft 2. 5 2 _ 3 ft

62 1 _ 5 ft

1. 4 2 _ 3 ft 2. 4 3 _ 4 ft

71 7 _ 8 ft

P 10•1

Name


Quick Check

10-1

1. Which fraction rounds to 5?

A 5 2 _ 3

B 5 1 _ 2

C 5 9 __ 20

D 4 9 __ 20

2. Estimate 3 4 _ 5 2 2 1 _ 3 .

A 1

B 2

C 5

D 6

3. Taylor has 16 1 _ 4 yd of crepe paper. He uses 4 5 _ 6 yd to make party decorations. Estimate how many yards of crepe paper he has left.

A 11 yd

B 12 yd

C 13 yd

D 21 yd

4. WritingtoExplain Describe three ways to estimate sums by answering the questions below. Then estimate each sum. Label 1 __ 12 , 5 _ 6 , 1 5 _ 8 , and 2 1 _ 6 on the number line. Explain how to use the number line to estimate 1 5 _ 8 1 2 1 _ 6 . How could you estimate 1 5 _ 8 1 2 1 _ 6 without using the number line? Explain how to use benchmark fractions to estimate 1 __ 12 1 5 _ 6 .

0 1 _ 2 1 1 1 _ 2 2 2 1 _ 2

Q 10•1

79

29 10

n n n n n n n n

5,600

Name


Daily Common Core Review10-2

1. �It�takes�4�pounds�of�grapes�to�make�1�pound�of�raisins.�How�many�pounds�of�grapes�would�you�need�to�make�3,000�pounds�of�raisins?�

A 1,000�pounds

B 6,000�pounds

C 9,000�pounds

D 12,000�pounds

2. �What�number�represents�n�in�the�diagram�below?

A 7

B 80

C 700

D 800

3. �What�equation�is�modeled�with�this�number�line?

A ��7�__�9��–��5�__�

9��=��2�__�

9��

B ��7�___�10

��–��5�___�10

��=��2�___�10

��

C ��2�__�7��+��5�__�7��=��7�__�7��

D ��2�__�9��+��5�__�

9��=��7�__�

9��

4. �What�is�the�least�common�denominator�of��9�__�15��and��2�_�3��?�

5. �Jen�needs�to�save�$360�for�a�new�camping�tent.�She�is�able�to�save�$15�each�week.�How�many�weeks�will�Jen�need�to�save�to�reach�her�goal?�Draw�a�picture�and�write�an�equation�to�solve�the�problem.�Explain�how�you�found�your�answer.

D 10•2

1

18

18

18

18

18

18

18

1

18

18

18 1

1

15

15

15

15

15

15

Name


Practice

10-2Modeling Addition and Subtraction of Mixed NumbersFor 1 and 2, use each model to find each sum or difference.

1. 1 3 __ 8 + 1 7 __

8 2. 3 1 __ 5 – 1 4 __ 5

Use fraction strips to find each sum or difference. Simplify, if possible.

3. 2 1 __ 3 + 1 2 __

3 4. 3 5 __

6 + 4 3 __

6 5. 5 1 __

4 – 1 2 __

4 6. 12 3 __

8 – 2 5 __

8

7. 8 1 __ 6 – 3 5 __

6 8. 4 6 ___

10 + 5 7 ___

10 9. 7 1 __

9 – 4 2 __

9 10. 6 2 __ 5 + 3 4 __ 5

11. 1 1 __ 6 + 3 5 __

6 12. 2 4 __

9 + 6 7 __

9 13. 6 3 __ 5 – 4 3 __ 5 14. 5 1 __

3 – 4 2 __

3

15. Jerome’s rain gauge showed 13 9 __ 10 centimeters (cm) at the end of last month.

At the end of this month, the rain gauge showed 15 3 __ 10 centimeters. How many

more centimeters of rain fell this month?

A 29 2 ___ 10

cm B 15 3 ___ 10

cm C 2 4 ___ 10

cm D 1 4 ___ 10

cm

16. You are adding 3 2 _ 3 + 2 2 _ 3 using fraction strips. Explain how you rename the

fraction part of the problem.

P 10•2

1

1

1

16

16

16

16

16

1

16

16

16

Name


Quick Check

10-2

3. Lou used 3 1 __ 8 cups of oats and 1 3 _ 8 cups of raisins in a recipe.

How many more cups of oats did Lou use than raisins?

A 1 1 __ 4 more cups

B 1 3 __ 4 more cups

C 4 1 __ 2 more cups

D 5 1 __ 2 more cups

4. WritingtoExplain Use the models of mixed numbers below to answer a and b.

a Write a mixed number for each model.

b Explain how you can use the models to find how much greater one mixed number is than the other.

1. What is the sum of 6 7 __ 8 + 4 5 __

8 ?

A 10 1 __ 8

B 10 1 __ 2

C 11 1 __ 2

D 11 5 __ 8

2. What is the difference of 5 1 _ 5 − 2 3 _ 5 ?

A 2 3 __ 5

B 2 1 __ 2

C 1 4 __ 5

D 1 3 __ 5

For 1 through 3, use fraction strips to find each sum or difference.

Q 10•2

Name



1. �Find�the�difference.�Simplify,�if�possible.

��4�___�12

��–��2�__�9��

A ��1�_�9��

B ��2�__�12��

C ��4�__�36��

D ��12�___�108��

2. �After�Ronaldo’s�Fourth�of�July�party,��2�_�3��of�his�cake�is�left.�How�much�cake�will�be�left�after�his�cousin�Max�eats�another��1�_�6��?�Simplify�your�answer�if�possible.

A ��5�_�6��

B ��1�_�2��

C ��1�_�3��

D ��3�__�12��

3. �Noreen�bought�two�shirts�for�$13�each�and�two�pairs�of�shoes��for�$18�a�pair.�How�much�did��she�pay�in�all?�

A $31

B $44

C $49

D $62

4. �A�day�pass�at�a�theme�park�costs�$16�for�children�and�$24.50�for�adults.�How�much�would�it�cost�to�get�day�passes�for�1�adult�and�2�children?�

5. �Eric�uses�3��5�_�8��yards�of�material�to make�a�shirt.�Which�is�3��5�_�8��written�as�an�improper�fraction?

A ��16�__�8��

B ��29�__�8��

C ��35�__�8��

D ��43�__�8��

D 10•3

Name


Practice

10-3Adding Mixed NumbersIn 1 through 6, find each sum. Simplify, if possible. Estimate for reasonableness.

1. 7 2 __ 3 + 8 5 __

6 2. 4 3 __

4 + 2 2 __ 5

3. 11 9 ___ 10

+ 3 1 ___ 20

4. 7 6 __ 7 + 5 2 __ 7

5. 5 8 __ 9 + 3 1 __

2 6. 21 11 ___

12 + 17 2 __

3

7. Write two mixed numbers that have a sum of 3.

8. What is the total measure of an average man’s brain and heart in kilograms (kg)?

9. What is the total weight of an average woman’s brain and heart in pounds (lb)?

10. What is the sum of the measures of an average man’s brain and an average woman’s brain in kilograms?

11. Which is a good comparison of the estimated sum and the actual sum of 7 7 _ 8 + 2 11

__ 12 ?

A Estimated < actual C Actual > estimated

B Actual = estimated D Estimated > actual

12. Can the sum of two mixed numbers be equal to 2? Explain why or why not.

Vital Organ Measures

Average woman’s brain 1 3 ___ 10

kg 2 4 __ 5 lb

Average man’s brain 1 2 __ 5 kg 3 lb

Average human heart 3 ___ 10

kg 7 ___ 10

lb

P 10•3

1 cup

2 cups

2 tablespoons

1 cups34

1 cups23

1 cups14

bread flour

whole-wheat flour

milk

water

sugar

yeast

Recipe

Name


Quick Check

10-3

3. Mr. Romano walks 1 7 __ 10 miles from his home to the train station.

Then he takes the train 9 5 _ 6 miles to work. How many total miles

does Mr. Romano travel to get to work?

A 11 8 ___ 15

B 11 1 __ 5

C 10 3 __ 4

D 10 8 ___ 15

4. WritingtoExplain A recipe calls for bread flour and whole-wheat flour. What is the total amount of flour used in the recipe? Express your answer as a mixed number in simplest form. Show your work.

1. What is the sum of 4 1 _ 5 and 2 3 _ 4 ?

A 6 7 __ 8

B 6 19 ___ 20

C 7 1 ___ 10

D 7 1 ___ 20

2. Find the sum of 3 3 _ 8 1 1 5 _ 6 .

A 4 5 ___ 12

B 4 5 ___ 24

C 5 5 ___ 24

D 5 1 __ 4

Q 10•3

Name



1. �What�number�is�missing�from�the�pattern?

2.01 4.03 ? 8.07 10.09

A 2.05

B 4.05

C 6.05

D �6.07

2. �Neil�spends�1��1�_�4��hours�washing�

the�car�and�2��5�_�8��hours�mowing�and�

weeding�the�yard.�How�many�

total�hours�does�he�spend�on�his�

chores?�Simplify�your�answer�if�

possible.

A 3��3�_�8��

B 3��5�_�8��

C 3��6�_�8��

D 3��7�_�8��

3. �Which�of�the�fractions�is�equal�to��4�_�5��?

A ��16�___�20

��

B ��16�___�25

��

C ��12�___�20

��

D ��8�___�15

��

4. �Mr.�DeWitt�carved�a�wooden�boat�for�his�granddaughter.�He�began�with�a�piece�of�wood�that�was�20.3�centimeters�long.�The�boat�is�16.7�centimeters�long.�How�many�centimeters�did�Mr.�DeWitt�carve�off�the�length�of�the�wood�when�he�made�the�boat?

5. �The�distance�between�Miami�and�Naples�is�107�miles.�The�distance�between�Miami�and�Jacksonville�is�about�three�times�this�distance.�Landon�estimates�that�the�distance�between�Miami�and�Jacksonville�is�about�400�miles.�Is�Landon’s�estimate�reasonable?�Why�or�why�not?

D 10•4

Name


Practice

10-4Subtracting Mixed NumbersFor 1 through 10, find each difference. Simplify, if possible.

1. 10 3 __ 4

− 7 1 __ 4

2. 7 3 __ 7

− 2 8 ___ 21

3. 3

− 2 2 __ 3

4. 17 7 __ 8

− 12 3 ___ 12

5. 9 5 __ 9 − 6 5 __

6 6. 4 3 __

4 − 2 2 __

3

7. 6 1 __ 4 − 3 1 __

3 8. 5 1 __ 5 − 3 7 __

8

9. 8 2 __ 7 − 7 1 __ 3 10. 2 9 ___

10 − 2 1 __

3

The table shows the length and width of several kinds of bird eggs.

11. How much longer is the Canada goose egg than the raven egg?

12. How much wider is the turtledove egg than the robin egg?

13. Which is the difference of 21 15 __ 16 − 18 3 _ 4 ?

A 2 7 ___ 16

B 2 9 ___ 16

C 3 3 ___ 16

D 3 9 ___ 16

14. Explain why it is necessary to rename 4 1 _ 4 if you subtract 3 _ 4 from it.

Egg Sizes in Inches (in.)

Bird Length Width

Canada goose 3 2 __ 5 2 3 ___

10

Robin 3 __ 4 3 __

5

Turtledove 1 1 __ 5 9 ___

10

Raven 1 9 ___ 10

1 3 ___ 10

P 10•4

347 feet

Name


Quick Check

10-4

3. Someofthelargestinsectsarebeetles.TheTitanusbeetlecanmeasure167__10centimetersinlengthandtheGiantWetabeetlecanmeasure81_2centimetersinlength.HowmuchlongeristheTitanusthantheGiantWeta?

A 251__5centimeters

B 91__5centimeters

C 82__3centimeters

D 81__5centimeters

4. WritingtoExplain Jessieisbuildingadoghouse.Foronesideoftheroof,sheneedsaboardthatis73_4feetlong.Shehasaboardthatmeasures91__12feet.Howmuchofthelengthdoessheneedtocutfromtheboard?Showyourworkandsimplifythefraction.

1. Whatisthedifferenceof61__514__5?

A 42__5

B 43__5

C 52__5

D 53__5

2. Findthedifferenceof81__945__

6.

A 31___18

B 35___18

C 41___12

D 45___18

Q 10•4

Name



1. �Which�mixed�number�is�represented�by�the�shaded�parts�of�the�model?�

A 2��1�__�2��

B 2��1�__�4��

C 1��3�__�4��

D 1��1�__�2��

2. �Which�of�these�is�the�correct�order�of�operations�for�evaluating�the�expression�3�+�4�×�22?

A �Add,�evaluate�the�term�with�an�exponent,�then�multiply

B �Add,�multiply,�then�evaluate�the�term�with�an�exponent

C �Evaluate�the�term�with�an�exponent,�add,�then�multiply

D �Evaluate�the�term�with�an�exponent,�multiply,�then�add

3. �The�Sunshine�Skyway�Bridge,�which�crosses�Tampa�Bay,�Florida,�is�the�world’s�longest�cable-stayed�bridge.�It�is�8,851.392�meters�long.�What�place�is�the�9�in�this�number?

A Hundreds

B Tenths

C Hundredths

D Thousandths

4. �Hector’s�father�is�4�times�as�old�as�Hector�and�twice�as�old�as�Carlos.�If�Carlos�is�24�years�old,�how�many�years�old�is�Hector?�

5. �Explain�the�difference�between�an�acute�angle�and�an�obtuse�angle.�In�your�explanation,�give�sample�measures�for�each�type�of�angle.

D 10•5

Name


Practice

10-5More Adding and Subtracting Mixed NumbersIn 1 through 13, simplify each expression.

1. 2 1 __ 8 + 4 2 __

3 2. 9 1 __

6 – 3 2 __

9 3. 8 1 __

4 – 6 5 __

8 4. 6 4 __ 5 + 5 3 ___

10

5. ( 3 1 __ 2 + 8 2 __

3 ) – 3 5 __

6 6. ( 14 1 __

6 – 4 5 __

9 ) + 1 7 ___

18 7. 7 7 ___

12 + ( 3 1 __

2 + 1 7 __

8 )

8. ( 10 1 __ 4 – 5 5 __

8 ) – 1 3 __

8 9. 100 3 ___

10 – 60 2 __

3 – 5 2 ___

15 10. 25 3 __

8 – ( 10 4 __ 5 + 5 7 __

8 )

11. ( 2 2 __ 3 + 4 5 __

6 ) + 3 3 __

8 12. ( 30 1 __

9 + 4 1 __

3 ) – 19 5 __

6 13. 7 2 __

3 + ( 5 1 __

6 – 1 5 __

9 )

14. Which shows three mixed numbers that have sum of 10?

A 1 2 __ 3 + 3 5 ___

12 + 4 3 __

4 C 2 3 __

8 + 5 1 __

2 + 1 1 __

4

B 3 1 __ 3 + 3 1 __

4 + 3 5 ___

12 D 5 1 __

4 + 1 7 __

8 + 3 7 __

8

15. What is a reasonable estimate for the sum of 4 1 __ 8 + 3 2 __

3 + 5 1 __

2 ?

16. Veronica is buying cubed cheese from Mr. Sand’s deli.

She asks for 1 3 __ 4 pounds. When Mr. Sand places some

cheese in a container and weighs it, the scale shows

1 1 __ 4 pounds. The container weighs 1 ___

16 pound. How many

more pounds of cheese would Mr. Sand need to add to

the scale to get the amount that Veronica asked for?

Explain how you solved the problem.

P 10•5

5625 in.h

235 in.

235 in.

Name


Quick Check

10-5

3. What is (9 1 __ 3 1 3 5 __

6 ) 5 1 __

6 ?

A 18 1 __ 3

B 8 5 __ 6

C 8

D 7

4. WritingtoExplain Emma made a rectangular picture frame

with a height of 25 5 __ 6 inches. The frame is 5 2 __

3 inches wide.

What is the height of the picture Emma placed in the picture

frame? Explain how you found your answer.

1. Which is the sum of 8 3 __ 4 1 2 1 __

2 ?

A 10 1 __ 4

B 10 1 __ 2

C 11 1 __ 6

D 11 1 __ 4

2. Which is the difference of

25 1 __ 8 12 3 __

4 ?

A 13 1 __ 8

B 13 2 __ 6

C 12 1 __ 3

D 12 3 __ 8

Q 10•5

3.3 feet

2.75 feet

Name

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5D 10•6


1. �Workers�at�the�Color-Right�Marker�Factory�pack�12�markers�in�each�box.�If�the�factory�makes�678�markers,�how�many�full�boxes�of�markers�can�the�workers�pack?�

A 50

B 56

C 57

D 62

2. �Perimeter�is�the�distance�around�a�figure.�What�is�the�perimeter�of�this�figure?�

A � 6.05�feet

B � 8.8�feet

C � 9.35�feet

D 12.1�feet

3. �The�table�below�shows�the�heights�of�four�friends.

Friends’Heights

Name Kay Leo Jay Ina

Height(feet) 5��3�_�8�� 5��1�_�2�� 4��3�_�4�� 4��7�__�12��

�Which�lists�the�friends�in�order�from�shortest�to�tallest?

A Jay,�Ina,�Leo,�Kay

B Kay,�Leo,�Jay,�Ina�

C Leo,�Jay,�Kay,�Ina

D Ina,�Jay,�Kay,�Leo

4. �How�many�degrees�does�a�right�angle�measure?

5. �Rita�finds�the�quotient�of�584�÷�7�to�be�82�R10.�Explain�why�her�answer�is�not�correct.�Then�find�the�correct�answer.

Name


Practice

10-6Problem Solving: Draw a Picture and Write an EquationDraw a picture and write an equation. Then solve.

3. Stewart draws a triangle, and each side is

2 1 _ 6 inches long. Judith draws a square, and each side

is 1 5 _ 8 inches long. Which figure has the greater perimeter,

the triangle or the square?

4. Cristoff practices playing his guitar for 1 1 _ 2 hours each weekday. He practices

this amount of time plus an additional 1 1 _ 2 hours on Sundays. Let x = the

number of hours Cristoff practices on Sundays. Draw a picture and write an

equation and solve to find the number of hours he practices on Sundays.

5. Which of these fractions, when added to 2 1 _ 3 , will give you a sum greater than six?

A 3 1 __ 2 B 3 5 ___

12 C 3 7 ___

12 D 3 3 __

4

6. Dennis says that 1 1 _ 2 , 1 2 _ 4 , and 1 3 _ 6 are all equivalent. Is he

correct? Draw a picture and explain your answer.

1. Mr. Flanders drives 1 2 _ 3 miles to

school and 1 2 _ 3 miles home each

day. He also drives an extra 2 2 _ 7

miles to go to the gym. How many

miles does he drive in one day?

2. Alison is making a 16-inch

necklace. The first 4 1 _ 4 inches are

filled with red beads and 8 3 _ 8 inches

are filled with blue beads. The rest

has white beads. How many inches

are filled with white beads?

P 10•6

Name


Quick Check

10-6

3. WritingtoExplain Silas is shipping two gifts to his

grandmother. The box and stuffing weigh 7 _ 8 of a pound and

one gift weighs 2 1 _ 4 pounds. The entire package weighs a total

of 8 23 __ 24 pounds. How many pounds does the other gift weigh?

Let n 5 the number of pounds the second gift weighs. Draw

a picture and write an equation to solve.

1. Todd biked 1 1 __ 10 miles to his friend’s

house. Then he biked 3 2 _ 3 miles

to the store and 4 4 _ 5 miles home. Which equation can you use to find out how far Todd biked?

A ( 4 4 __ 5 1 1 1 ___ 10

) − 3 2 __ 3 5 d

B 4 4 __ 5 − 3 2 __ 3 − 1 1 ___

10 5 d

C 4 4 __ 5 1 ( 3 2 __ 3 − 1 1 ___

10 ) 5 d

D 1 1 ___ 10

1 3 2 __ 3 1 4 4 __ 5 5 d

2. Students in a physical education

class are running a total of

4 7 __ 12 miles this week. Shayla has

run 1 2 _ 3 miles. Which equation can

you use to find out how much

farther Shayla needs to run?

A 4 7 ___ 12

1 4 7 ___ 12

5 r

B 4 7 ___ 12

− 1 2 __ 3 5 r

C 6 1 __ 4 − 1 2 __

3 5 r

D 4 7 ___ 12

1 1 2 __ 3 5 r

Q 10•6

topic 10 - mrs. stephanie evans class websitemr. romano walks 1 __7 10 miles from his home to the...

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