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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
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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
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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
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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
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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
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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
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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
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Daily Common Core Review10-3
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
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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
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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
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Daily Common Core Review10-4
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
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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
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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
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Daily Common Core Review10-5
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
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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.
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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
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Daily Common Core Review10-6
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.
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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
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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