Adding & Subtracting Fractions · Adding & Subtracting Fractions _____ ... Adding Fractions with ... Add the fractions to calculate the number of eggs used and

$Page 1: Adding & Subtracting Fractions · Adding & Subtracting Fractions _____ ... Adding Fractions with ... Add the fractions to calculate the number of eggs used and$
Topic 9 Adding & Subtracting

Fractions

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Test Date

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

Daily Common Core Review

9-1

A veterinarian weighed four cats. Use the data shown in the table for 1 through 3.

Weights of Cats

Cat Weight (pounds)

Bob 8.25

Fluffy 8 3 _ 4

Miss Kitty 8.5

Tiger 8

1. Which cat’s weight does point X name?

A Bob

B Fluffy

C Miss Kitty

D Tiger

2. Which cat’s weight in the table above is closest to 9 pounds?

A Bob

B Fluffy

C Miss Kitty

D Tiger

3. What is the difference between Bob’s weight and Miss Kitty’s weight?

A 0.20 pounds

B 0.25 pounds

C 0.35 pounds

D 0.75 pounds

4. Plot 0.29 on the number line below.

5. The table shows the number of miles a taxi drives and the cost of the taxi ride.

Distance (miles) 8 10 16 22

Cost $4 $5 $8 ?

Describe how to find the cost of a 22-mile taxi ride?

6. Write a whole number greater than 99,999,999 and less than 100,000,100.

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Practice

9-1Problem Solving: Writing to ExplainEstimate the fractional part of the shaded portions below. Explain how you decided.

1.

2.

3. Draw a square and shade about 1 _ 8 of it. How didyou decide how much to shade?

4. Draw two rectangles that are different sizes. Shade about 1 _ 2 of each. Are the shaded parts the same amount? Explain.

5. Look at a picture of the American flag. Approximately whatpart of the flag is blue? Explain.

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tomatoeslettucepumpkins cucumbers

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Quick Check

9-1

1. About how much of the pizza is covered with pepperoni?

A about 9 __ 10

B about 5 _ 6

C about 3 _ 8

D about 2 _ 3

2. Claire is painting a wall in her room white. About how much of the wall has she painted?

A about 3 _ 8

B about 3 _ 4

C about 7 _ 8

D about 9 __ 10

3. WritingtoExplain Estimate the part of the garden that is planted with tomatoes. Explain how you decided.

Q 9•1

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9-2

1. Bukka has 986 paperback books. He wants to put these books on storage shelves. Each shelf can hold 50 paperback books. How many shelves will Bukka need to hold all of the books?

A 20 shelves

B 19 shelves

C 18 shelves

D 10 shelves

2. The U.S. Census Bureau estimated that the population of St. Petersburg, Florida, in 2006 was 248,098. What is this number in expanded notation?

A 200,000 + 40,000 + 8

B 200,000 + 40,000 + 8,000 + 900 + 8

C 200,000 + 40,000 + 8,000 + 90 + 8

D 248,000 + 90 + 8

3. Which is the correct product of n × 7 if n = $0.25

A $3.25

B $2.75

C $1.75

D $2.25

4. What is the missing y-value in the table below?

x 2 4 6 8 10y 24 48 72 96 ?

5. Carter drew this number line to illustrate the sum of two fractions. He forgot to label the fractions.

What fraction equation did he draw? Explain how you know what number to use for the denominator.

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Practice

9-2Estimating Sums and Differences of FractionsIn 1 through 8, tell if each fraction is closest to 0, 1 _ 2 , or 1. You may use a number line to help.

1. 1 __ 9 2. 5 __

9 3. 11 ___

20 4. 6 ___

10

5. 6 __ 7 6. 5 ___ 12

7. 3 __ 4 8. 12 ___

15

In 9 through 16, estimate each sum or difference by replacing each fraction with 0, 1 _ 2 , or 1.

9. 7 ___ 12

+ 4 __ 5 10. 1 ___ 12

+ 2 __ 4 11. 4 __

9 – 1 __

6 12. 2 __

6 + 8 __

9

13. 1 __ 6 – 1 __

8 14. 2 __ 5 – 3 __ 7 15. 7 __

8 – 7 __

9 16. 5 ___

12 + 2 __ 5

17. Which is the best estimate for the

difference of 9 __ 16 – 4 _ 9 ?

A 1 – 1 = 0 C 1 – 1 __ 2 = 1 __

2

B 1 __ 2 – 1 __

2 = 0 D 0 – 0 = 0

18. Which fraction can NOT be

replaced with 1 _ 2 when estimating?

A 10 ___ 12

C 4 ___ 10

B 2 __ 6 D 13 ___

24

19. Mia estimated 5 _ 8 + 1 _ 9 by replacing 5 _ 8 with 1 and 1 _ 9 with 0. Her

estimated sum was 1 + 0 = 1. Explain why Mia’s estimate is

NOT accurate.

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Quick Check

9-2

5. WritingtoExplain Keri says that you can replace a fraction

with 0, 1 _ 2 , or 1 by looking at the denominator first. If the numerator

is half or close to half the value of the denominator, replace with 1 _ 2 .

If the numerator is closer to the value of the denominator, replace

with 1. Is Keri correct? Use the number line and 5 _ 8 as an example

to help you explain your reasoning.

1. Which fraction can be replaced

with 1 _ 2 when estimating with

fractions?

A 1 __ 8

B 2 __ 9

C 2 __ 3

D 10 ___ 12

3. Which is the BEST estimate for

the sum of 5 __ 12 + 2 _ 5 ?

A 0 + 0 = 0

B 1 __ 2 + 0 = 1 __

2

C 1 + 1 = 2

D 1 __ 2 + 1 __

2 = 1

2. Which fraction can be replaced

with 0 when estimating with

fractions?

A 1 __ 5

B 3 __ 4

C 8 ___ 20

D 4 __ 9

4. Which is the BEST estimate

for the difference of 7 _ 8 − 4 _ 9 ?

A 1 – 1 = 0

B 1 __ 2 – 1 __

2 = 0

C 1 – 1 __ 2 = 1 __

2

D 0 – 0 = 0

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9-3

1. Find the lowest common multiple of 5 and 8.

A 16

B 20

C 24

D 40

2. Which decimal is equal to 1 3 _ 4 ?

A 1.75

B 1.43

C 1.34

D 1.25

3. Use the diagram below.

x x x x x x x x

400

What is the value of x?

4. Casey’s watch beeps every 15 minutes. Her brother’s watch beeps every 10 minutes. The last time both watches beeped was at 5:30 p.m. What time will it be the next time both watches beep at the same time? Explain how you know.

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Practice

9-3Adding Fractions with Unlike DenominatorsFind each sum. Simplify if necessary.

1. 2 __ 9 + 1 __

3 2. 1 __ 7 + 3 ___

21 3. 2 __

3 + 1 __ 5

4. 1 __ 4 + 2 __

3 5. 1 ___

12 + 4 __

6 6. 1 __

2 + 2 __ 5

7. 1 __ 6 + 5 ___

12 8. 4 __

6 + 1 __ 3 9. 1 __ 5 + 1 __

8

10. 3 __ 4 + 1 __

9 11. 6 ___

12 + 1 __

3 12. 4 __

8 + 1 __

2

Jeremy collected nickels for one week. He is making stacks of

his nickels to determine how many he has. The thickness of one

nickel is 1 __ 16 inch.

13. How tall is a stack of 16 nickels?

14. What is the combined height of 3 nickels, 2 nickels, and 1 nickel?

15. What is the sum of 5 ___ 30

+ 4 __ 6 ?

A 5 __ 6 B 7 __

9 C 2 __

3 D 9 ___

12

16. How do you rename 2 _ 5 so you can add it to 11 __ 25 ? What is the sum?

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Quick Check

9-3

3. A piece of glass is 1 _ 4 inch thick, and a second piece of glass

is 7 __ 16 inch thick. What is the combined thickness of the two

pieces of glass?

A 11 ___ 16

inch

B 15 ___ 16

inch

C 1 3 ___ 16

inches

D 1 3 __ 4 inches

4. WritingtoExplain Anna bought a package of one dozen eggs at the store. She used 1 _ 4 of them to make cookies, and her brother used 1 _ 3 of them to make pancakes for the family. Add the fractions to calculate the number of eggs used and then determine how many eggs were left. Show your work.

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

A 5 __ 9

B 9 ___ 10

C 18 ___ 20

D 19 ___ 20

2. Find the sum of 1 __ 6 + 1 __

2 .

A 1 __ 3

B 1 __ 4

C 2 __ 3

D 3 __ 4

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9-4

1. Find the sum. Simplify if possible.

2 __ 5 + 3 __ 6

A 5 ___ 11

B 9 ___ 10

C 27 ___ 30

D 2 __ 3

2. The circumference of the moon, measured at its equator, is 10,921 kilometers. What digit is in the thousands place?

A 9

B 2

C 1

D 0

3. As of 2008, the record for the longest rabbit ear span ever measured was 31.125 inches. Toby’s pet rabbit has an ear span of 12.505 inches. How much longer, in inches, is the record measurement than the ear span of Toby’s pet rabbit?

4. Use compatible numbers to estimate the quotient of 3,780 ÷ 9. What compatible numbers did you use? Is your estimate an underestimate or overestimate? Explain why.

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Practice

9-4Subtracting Fractions with Unlike DenominatorsFind the difference. Simplify if necessary.

1. 10 ___ 12

− 1 __ 4 2. 9 ___

10 − 3 __ 5 3. 7 __

8 − 2 __

6

4. 7 ___ 12

− 1 __ 4 5. 4 __ 5 − 1 __

3 6. 2 __

3 − 1 __

6

7. 4 __ 8 − 1 __

4 8. 4 ___

10 − 1 __ 5 9. 9 __

9 − 2 __

3

10. 9 ___ 15

− 1 __ 3 11. 4 ___

12 − 1 __

6 12. 14 ___

20 − 3 __ 5

13. The pet shop owner told Jean to fill her new fish tank 3 _ 4 full with water. Jean filled it 9 __ 12 full. What fraction of the tank does Jean still need to fill?

14. Paul’s dad made a turkey potpie for dinner on Wednesday. The family ate 4 _ 8 of the pie. On Thursday after school, Paul ate 2 __ 16 of the pie for a snack. What fraction of the pie remained?

15. Gracie read 150 pages of a book. The book is 227 pages long. Which equation shows the amount she still needs to read to finish the story?

A 150 − n = 227 C n − 150 = 227

B 227 + 150 = n D n + 150 = 227

16. Why do fractions need to have a common denominator before you add or subtract them?

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Quick Check

9-4

3. A 1 _ 2 yard of ribbon is needed for a craft project. How much ribbon will remain from a piece that measures 7 _ 8 yard?

A 3 ___ 16

yard

B 1 __ 4 yard

C 1 __ 6 yard

D 3 __ 8 yard

4. WritingtoExplain You have a cake that was cut into 18 pieces. At the end of your party, one half of the cake was left. Then your friend took 5 pieces home for her family. What fraction of the cake do you still have? Simplify if necessary. Show your work.

1. What is the difference of

4 __5 − 1 __ 4 ?

A 2 __ 3

B 9 ___ 10

C 11 ___ 20

D 19 ___ 20

2. Find the difference of

2 __3 − 1 __

6 .

A 5 __ 9

B 1 __ 2

C 1 __ 4

D 1 __ 3

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9-5

1. �A�bank�charges�5.25672%�annual�percentage�rate�on�a�home�mortgage.�What�is�this�number�rounded�to�the�nearest�tenth?�

A 5.2�

B 5.25

C 5.3

D 6

2.

�What�fraction�of�the�rectangle�is�shaded?�

A ��2�_�8��

B ��4�_�8��

C ��3�_�6��

D ��5�_�8��

3. �How�would�you�get�the�variable�alone�in�the�equation�4y�5�3?�

A �Divide�both�sides�of�the�equation�by�4

B �Add�4�to�both�sides�of�the�equation

C �Multiply�both�sides�of�the�equation�by�4

D �Subtract�3�from�both�sides�of the�equation

4. �Draw�a�picture�to�show��4�_�7��as�a�part�of�a�set.�

5. �Evaluate�the�expression�for�m�5�2.5m�1�2(m�+�8)�+�3

6. �Carla�checked�8�books�out�of�the�library.�This�was�3�more�than�Lee�checked�out.�How�many�books�did�Lee�check�out�of�the�library?�Write�an�equation�to�solve�the�problem,�then�write�the�answer.

7. �Jim’s�book�club�offers�1�free�book�for�every�4�books�he�buys.�How�many�books�would�Jim�have�to�buy�to�get�6�free�books?

Booksbought

4 8 12 16 20

Freebooks

1 2 3 4 5 6

�

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Practice

9-5More Adding and Subtracting FractionsFind each sum or difference. Simplify your answer.

1. 5 _ 6 1 4 __ 12 5 2. 4 _ 5 2 1 __ 10 5 3. 5 __ 12 1 2 _ 3 5

4. 9 __ 20 1 3 _ 5 5 5. 6 __ 16 2 1 _ 4 5 6. 19 __ 21 2 2 _ 7 5

7. 2 _ 5 1 5 __ 20 5 8. 8 _ 9 2 5 __ 12 5 9. 7 _ 8 1 11 __ 24 2 5 _ 6 5

10. Number Sense Is 7 _ 8 or 11 __ 10 closer to 1? How did you decide?

Emma has a small garden. Emma’s garden is 1 _ 5 beans, 1 _ 8 peas, and 1 _ 2 corn. The rest is planted with flowers.

11. What fraction of Emma’s garden is planted with vegetables?

12. Are there more flowers or peas in Emma’s garden?

13. To solve the subtraction sentence 17 __ 10 2 2 _ 5 5 ?, which common denominator is the best choice?

A 10

B 15

C 20

D 50

14. Writing to Explain To find the sum of 4 _ 9 and 7 __ 12 , Mario rewrites the fractions as 8 __ 36 and 21 __ 36 . His answer is 29 __ 36 . Is Mario right? If not, show his error and correct it.

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Quick Check

9-5

1. Find 1 _ 4 1 1 _ 6 .

A 1 _ 2 B 5 __ 12

C 1 _ 3 D 1 _ 5

2. Find 2 _ 3 2 5 _ 8 .

A 1 __ 24 B 1 _ 8

C 11 __ 24 D 3 _ 5

3. The picnic area in a park is on the trail that connects the parking lot with the lake. The picnic area is 2 _ 5 mi from the parking lot and 1 _ 3 mi from the lake. How long is the trail?

A 1 _ 5 mi B 1 _ 2 mi

C 11 __ 15 mi D 4 _ 5 mi

4. WritingtoExplain A gallery used this floor plan to display art.What fraction names each display area? hint: Each numeratoris 1 and the smallest sections show 1 __ 24 . Write one question about the floor plan that can be answered by writing an addition sentence and one question that can be answered by writing a subtraction sentence. Answer your questions.

Paintings

Metal

Special Exhibits

Glass

Sculpture

ClothMaterials

Cloth Materials Glass Metal

Paintings SculptureSpecial Exhibits

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9-6

1. How many pairs of parallel sides are in a parallelogram?

A 1

B 2

C 3

D 4

2. The area of the state of Florida is 53,927 square miles. What is this number rounded to the nearest thousand?

A 50,000

B 53,000

C 53,900

D 54,000

3. How many lines of symmetry can be found in the figure below?

4. Every weekday, Tasha walks 3 _ 8 mile to school. After school, she walks 2 _ 8 mile to her grandparents’ house. Then she takes the same route home. Does Tasha walk more than one mile each day? Explain how you know.

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Practice

9-6More Adding and Subtracting FractionsIn 1 through 12, simplify each expression.

1. 4 __ 6 + 2 __

9 2. 2 __ 7 + 1 __

2 3. 8 ___

12 + 1 __

6 4. 3 __

8 + 1 __

6

5. 1 ___ 12

+ 7 __ 9 6. 4 ___

18 + 2 __

9 7. 1 __

3 + 1 __

4 8. 5 ___

15 + 3 __ 5

9. 1 __ 2 – ( 1 __

8 + 1 __

8 ) 10. 3 __

4 + ( 1 __

4 – 1 __

6 ) 11. ( 1 __

2 + 3 ___

20 ) – 2 ___

20 12. ( 2 __ 5 + 1 __ 5 ) – 3 ___

10

13. A plumber is fitting a water pipe

that is 3 _ 4 foot long on to a water

pipe that is 2 __ 12 foot long. How long

will the finished pipe be?

A 11 ___ 12

foot C 2 ___ 12

foot

B 8 ___ 16

foot D 1 foot

14. Joel made some muffins.

He gave 1 _ 4 of the muffins to a

neighbor. He took 3 _ 8 of the muffins

to school. What fraction of the

muffins is left?

A 4 ___ 12

C 5 ___ 12

B 3 __ 8 D 8 __

8

15. Carl has three lengths of cable, 5 _ 6 yard long, 1 _ 4 yard long,

and 2 _ 3 yard long. He needs at least 1 yard of cable.

a Which two pieces together make a length at least 1 yard and closest to 1 yard?

b If Carl uses the two shortest pieces, how much more cable would he need?

c After Carl has used 1 yard of cable, how much cable will he have left? Explain how you found your answer.

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Quick Check

9-6

1. What is the sum of 1 _ 3 + 1 _ 3 + 1 _ 8 ?

A 3 ___ 14

B 3 ___ 11

C 19 ___ 24

D 6 __ 8

2. What is the difference of 7 _ 8 – 1 _ 3 ?

A 6 __ 5

B 8 ___ 11

C 6 __ 8

D 13 ___ 24

3. A recipe for crumb cake says to mix 3 _ 8 cup of brown sugar

and 1 _ 3 cup of white sugar. From this sugar mixture, set

aside 1 _ 4 cup for the crumb topping. The remaining sugar

mixture is used to make the cake. What amount of the

sugar mixture is used to make the cake?

A 11 ___ 24

cup

B 1 __ 2 cup

C 7 ___ 12

cup

D 17 ___ 24

cup

4. WritingtoExplain Owen and Bella shared a granola bar.

Bella ate 1 _ 4 of the granola bar. Owen ate 1 _ 3 of the bar.

a Explain how to find the fraction of the granola bar that Owen and Bella ate.

b Explain how to find the fraction of the granola bar that is left.

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9-7

1. A deli is open 5 days a week for 5 hours each day. One week the deli served 925 customers. If the same number of customers were served each hour, how many were served each hour?

A 185

B 125

C 37

D 16

2. Which number completes the equation below?

(24 − 1) + 21 = + 14 + 3 × 5

A 6

B 7

C 14

D 35

3. Choose a fraction to make the inequality true.

3 __ 5 >

A 4 __ 5

B 3 __ 6

C 4 __ 6

D 5 __ 6

4. Mr. Rosenthal is getting ready to make gumbo, a type of soup. He buys some shrimp for $7.95, an onion for $0.26, and a bunch of celery for $1.03. How much does he spend on ingredients?

5. What is the missing number in this equation? Explain how you know.

2 × (10 × 3) = ( × 10) × 3

What property does the equation illustrate?

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x pounds in all

x pounds in all13

512

16

26

26

16

x pounds in all3

125

126

12

x pounds in all1

121

125

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Practice

9-7Problem Solving: Draw a Picture and Write an EquationDraw a picture and write an equation to solve.

1. Jamie bought 5 _ 8 pound of wheat flour. He also bought 1 _ 4 pound of white flour. How much flour did he buy?

2. Katie is 3 _ 5 of the way to Brianna’s house. Larry is 7 __ 10 of the way to Brianna’s

house. How much closer to Brianna’s house is Larry?

3. Nina practiced the trumpet for 1 _ 6 hour. Santiago practiced the trumpet for

2 _ 3 hour. How much longer did Santiago practice than Nina?

4. Ned caught 1 _ 3 pound of fish. Sarah caught 5 __ 12 pound of fish. Jessa caught

1 _ 6 pound of fish. Which bar diagram shows how to find how many pounds

of fish they caught in all?

A C

B D

5. In solving a fraction equation, John added the numerators of several fractions with unlike denominators. What should John have done first?

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Quick Check

9-7

For 1 and 2, you may draw a picture and write an equation to help.

1. Betty mixed 1 _ 6 pound of peanuts with 1 _ 3 pound of raisins.

How much mix did Betty have in all?

A 1 __ 4 pound C 1 __

2 pound

B 1 __ 3 pound D 1 pound

2. Jill did aerobics for 3 _ 5 hour and then lifted weights for 1 _ 3 hour.

How much exercise did Jill get?

A 14 ___ 15

hour C 2 __ 5 hour

B 4 __ 5 hour D 1 __ 5 hour

3. Justin used 3 _ 4 pound of broccoli to make a stir-fry and 9 __ 10 pound

of broccoli to make cheddar and broccoli soup. Which picture

can be used to find how much broccoli Justin used in all?

A 9 ___ 10

3 __ 4 x

C

9 ___ 10

?

x

B x

3 __ 4 9 ___

10

D 3 __ 4

9 ___ 10

x

4. WritingtoExplain Matt jogged 1 _ 2 of a mile. Thomas jogged 5 _ 8 of a mile. How

much farther did Thomas jog? Draw a picture and write an equation to solve.

Q 9•7

Adding & Subtracting Fractions · Adding & Subtracting Fractions _____ ... Adding Fractions with ... Add the fractions to calculate the number of eggs used and

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