Adding & Subtracting Fractions · Adding & Subtracting Fractions _____ ... Adding Fractions with...
Transcript of Adding & Subtracting Fractions · Adding & Subtracting Fractions _____ ... Adding Fractions with...
Topic 9 Adding & Subtracting
Fractions
_________ Name
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Test Date
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8 9
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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.
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Daily Common Core Review
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
Q 9•2
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Daily Common Core Review
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
Q 9•3
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Daily Common Core Review
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
Q 9•4
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Daily Common Core Review
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
Q 9•5
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Daily Common Core Review
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.
Q 9•6
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Daily Common Core Review
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
12
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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