Topic 11 - Weebly€¦ · D The 34th traveler in line 2. Shannon says, “My apartment number is a prime number.” Which could be Shannon’s apartment number? A 115 B 273 C 317

Topic 11 Multiplying/&

Dividing Fractions

_________ Name

___________ Test Date

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Daily Common Core Review11-1

1. Airport security guards choose some travelers for an extra safety check. So far, the guards have chosen the 6th, 12th, 18th, and 24th travelers in line. Which of these people will most likely be chosen for the extra safety check?

A The 25th traveler in line

B The 26th traveler in line

C The 30th traveler in line

D The 34th traveler in line

2. Shannon says, “My apartment number is a prime number.” Which could be Shannon’s apartment number?

A 115

B 273

C 317

D 414

3. Ms. Royal left for work at 7:48 a.m. She reached her office at 8:23 a.m. How long did Ms. Royal take to get to her office?

A 25 minutes

B 35 minutes

C 1 hour 25 minutes

D 1 hour 35 minutes

4. What are the next three numbers in this pattern?

10,9 1 ___ 10

, 8 2 ___ 10

, 7 3 ___ 10

, , ,

5. The table shows how much work four students have done on their homework.

List the students in order from greatest to least fraction of work done.

6. Write 5 9 __ 25 as an improper fraction.

StudentNumberofPages

Done

TotalNumberofPages

ToDoGina 1 3

Marcus 2 4Emily 3 5Jaime 4 6

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Practice

11-1Multiplying Fractions and Whole NumbersFind each product.

1. 1 __ 4 of 96 5 2. 4 __

7 of 28 5 3. 3 __

4 3 72 5

4. 45 3 3 __ 9 5 5. 56 3 7 __

8 5 6. 42 3 3 __

7 5

7. 1 __ 2 of 118 5 8. 3 __

8 of 56 5 9. 1 ___

10 3 400 5

10. 84 3 1 __ 6 5 11. 64 3 5 ___

16 5 12. 40 3 11 ___

20 5

13. 5 __ 8 of 48 5 14. 1 __

7 of 77 5 15. 4 __

5 3 90 5

16. 42 3 3 ___ 14

5 17. 72 3 5 __ 8 5 18. 18 3 2 __

3 =

19. 5 __ 6 3 84 5 20. 11 ___

12 3 144 5 21. 6 __

7 3 42 5

22. Complete the table by writing the product of each expression in the box below it. Use a pattern to find each product. Explain the pattern.

23. Reasoning If 1 _ 2 of 1 is 1 _ 2 , what is 1 _ 2 of 2, 3, and 4?

24. Which is 2 _ 3 of 225?

A 75 B 113 C 150 D 450

25. Explain It Explain why 1 _ 2 of 2 equals one whole.

1 _ 2 3 32 1 _ 4 3 32 1 _ 8 3 32 1 __ 16 3 32

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Quick Check

11-1

1. Calculate the product: 4 __ 5 3 55.

A 11

B 44

C 50

D 75

2. Calculate the product: 2 __ 9 3 63.

A 7

B 14

C 18

D 45

3. Marcy is making cookies. For each batch of dough, she needs 2 _ 3 cup of sugar. How much sugar will she use if she makes 6 batches of cookies?

A 2 cups

B 3 cups

C 4 cups

D 6 cups

4. Jonathan is making a square picture frame that measures 3 _ 4 foot on each side. If he plans to cut each of the 4 sides from one piece of molding, how long must it be?

A 1 1 _ 2 feet

B 3 feet

C 4 feet

D 4 1 _ 4 feet

5. WritingtoExplain Canned beans are on sale at a price of 5 cans for $3, which means each can will cost 3 _ 5 of a dollar. Your club needs 35 cans of beans for a large chili dinner. How much will the beans cost? Show your work.

Q 11•1

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1. Which decimal is greater than 2.234?

A 2.03

B 2.129

C 2.13

D 2.241

2. Evaluate the expression.

(7 × 2 + 22) ÷ 9

A 18

B 9.5

C 2

D 1.5

3. Evaluate the following expression for n = 8.

4 + (n – 2) ÷ 3

A 10

B 6

C 3.3

D 1

4. Round the number to the nearest thousandth.

5.7935

A 5.8 C 5.793

B 5.794 D 5.79

5. A movie rental store rents DVDs for $3.50 each. How much will the store make after it rents 22 DVDs?

A $66 C $75

B $70 D $77

A farmer is selling 480 sheep. Half of the sheep are sold to a neighboring farm that has 150 acres. One-third of the sheep are sold to his son who is starting his own farm of 240 acres.

6. How many sheep are sold to the neighboring farm?

7. How many sheep are sold to his son?

8. How many sheep does the farmer have left to sell?

9. What is the area of the playground shown below?

20 feet

5 feet

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Practice

11-2Multiplication as ScalingIn 1-20, without multiplying, decide which symbol belongs in the box: <, >, or =.

1. 2 1 _ 2 × 3 2 _ 3 3 2 _ 3

3. 4 _ 5 × 4 2 _ 3 4 2 _ 3

5. 5 3 _ 5 × 2 _ 2 5 3 _ 5

7. 6 1 _ 2 × 7 2 _ 3 7 2 _ 3

9. 3 _ 5 × 8 4 _ 5 8 4 _ 5

11. 9 2 _ 7 × 3 _ 3 9 2 _ 7

13. 1 _ 3 × 1 2 _ 5 1 2 _ 5

15. 2 3 _ 5 × 4 _ 4 2 3 _ 5

17. 3 1 _ 3 × 4 2 _ 7 4 2 _ 7

19. 5 1 _ 2 × 6 2 _ 3 5 1 _ 2

2. 1 _ 3 × 9 2 _ 5 9 2 _ 5

4. 1 3 _ 5 × 6 _ 6 1 3 _ 5

6. 2 1 _ 3 × 3 2 _ 7 3 2 _ 7

8. 4 1 _ 2 × 5 2 _ 3 5 2 _ 3

10. 3 _ 5 × 6 4 _ 5 6 4 _ 5

12. 7 2 _ 7 × 7 _ 7 7 2 _ 7

14. 1 _ 3 × 8 2 _ 5 8 2 _ 5

16. 9 3 _ 5 × 3 _ 3 9 3 _ 5

18. 1 2 _ 3 × 2 2 _ 5 2 2 _ 5

20. 3 1 _ 3 × 4 _ 4 3 1 _ 3

21. Put the following products in order from least to greatest, without multiplying.

5 × 3 _ 4 , 4 1 _ 4 × 3 _ 4 , 1 _ 2 × 3 _ 4 , 3 _ 3 × 3 _ 4

22. Put the following products in order from greatest to least, without multiplying.

6 × 2 _ 5 , 3 2 _ 3 × 2 _ 5 , 2 _ 7 × 2 _ 5 , 2 _ 2 × 2 _ 5

23. Melissa and her friends are stretching rubber bands for an activity in science class. Melissa stretched her elastic to 10 inches. Juan stretched it 3 1 _ 2 times as far. Sara stretched it 4 _ 4 as far. Marsha stretched it 2 _ 5 as far. Put the students in order of how far they stretched their rubber bands from least to greatest.

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Quick Check

11-2

For 1-3, without multiplying, decide which symbol belongs in the box: <, >, or =.

1. 2 1 _ 2 × 1 1 _ 2 1 1 _ 2

2. 3 _ 5 × 1 2 _ 7 1 2 _ 7

3. 6 3 _ 4 × 5 _ 5 6 3 _ 4

4. Writing to Explain Gloria and her friends are rolling out modeling clay for an activity in math class. Gloria rolled out her clay until it was 18 inches long. Michaela rolled hers 2 1 _ 2 times as far. Kris rolled hers 3 _ 3 as far. Sammi rolled hers 4 _ 7 as far. Put the students in order of the length of their clay from least to greatest. Explain how you found your answer.

Q 11•2

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1. Some campers voted for the type of food they would like to have at their end-of-summer party. Aiden reported the results in the table below. Which food had the most votes?

Pizza 0.35

Wraps 0.15

Tacos 1 __ 6

Burgers 1 _ 3

A Pizza

B Wraps

C Tacos

D Burgers

2. There are twice as many boys as girls on Carrie’s school bus. Which fraction of the students on the bus are boys?

A 3 _ 2

B 2 _ 3

C 1 _ 2

D 1 __ 3

3. Now there are 22 students in Latisha’s class. Since the start of school, 2 students have joined the class and 4 students have moved away. How many students were in Latisha’s class at the beginning of the school year?

A 22 students

B 20 students

C 24 students

D 28 students

4. The sum of the values of five coins is $0.85. What are the five coins?

5. Tell whether an exact answer or an estimate is needed. Then solve.

Dinah has $206.72 in her savings account. She deposits $45.10. How much is in her account now?

6. Order these numbers from least to greatest.

1.5 1.15 1.51 1.1

7. Evaluate 2y 1 4 for y 5 15.

8. Find 60 3 0.75.

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Practice

11-3Estimating Products Estimate each product.

1. 2 3 _ 8 3 1 _ 3 2. 6 3 2 1 _ 5 3. 6 __ 10 3 5 3 _ 4

4. 3 7 _ 9 3 6 2 _ 5 5. 2 1 _ 2 3 2 1 _ 3 6. 7 _ 8 3 4 3 _ 8

7. 27 3 3 _ 8 8. 1 _ 4 3 17 9. 3 _ 5 3 51

10. 8 4 _ 9 3 3 6 _ 7 11. 12 __ 15 3 8 12. 17 3 1 _ 2

13. 1 _ 3 3 2 4 __ 10 14. 7 5 __ 8 3 2 2 _ 3 15. 5 __ 12 3 12

16. Show three ways to estimate 3 _ 5 3 9 1 _ 2 . Identify each method you use.

17. Jenna lives 4 3 __ 10 miles from school. She estimates that she travels4 3 2 3 5, or 40 miles each week. Is her estimate an overestimateor an underestimate? Explain.

18. Which benchmark fraction could you use to estimate the product of 36 3 11 __ 16 ? ____

19. Estimation Which is the best estimate for the area of a square with sides equal to 4 1 _ 8 inches?

A 6 sq in.

B 12 sq in.

C 16 sq in.

D 20 sq in.

20. Bryce has 24 baseball trophies. Matt has 3 _ 4 as many trophies as Bryce. How many trophies does Matt have?

A 6 trophies

B 12 trophies

C 18 trophies

D 24 trophies

184

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Quick Check

11-3

1. Which would give the best estimate of 4 7 __ 8 3 3 6 __ 7 ?

A 12

B 15

C 16

D 20

2. Which estimate of 7 __ 10 3 16 uses a benchmark fraction?

A 1 3 16 516

B 7 __ 10 3 20 5 14

C 3 __ 4 3 16 5 12

D 7 __ 10 3 10 5 7

3. Fruit juice makes up 2 __ 3 of the liquid ingredients in Alonzo’s punch recipe. Estimate how many gallons of fruit juice are needed to make 8 1 __ 2 gallons of punch.

A 3 gallons

B 6 gallons

C 9 gallons

D 16 gallons

4. WritingtoExplain Cassidy has 10 feet of string. She uses 5 __ 8 feet of string for each bracelet she makes. Does she have enough string to make 15 bracelets? Estimate 5 __ 8 3 15 to solve the problem. Then explain how you made your estimate and why you chose that method of estimation.

Q 11•3

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1. Find the product: 2 __ 3 of 12.

A 72

B 18

C 9

D 8

2. Jenny spent 24 days at Granny’s house last summer. Her sister spent 3 _ 8 of that time at Granny’s. How many days did Jenny’s sister spend at Granny’s house last summer?

A 6

B 9

C 14

D 64

3. Which decimal is equal to 34 ____ 100

?

A 3.4

B 0.34

C 0.034

D 0.0034

4. Edgar went to physical education class 72 times this year. He spent 3 _ 4 of those classes outside. How many of Edgar’s physical education classes this year were held outside?

5. During 5 _ 8 of those physical education classes, Edgar played games involving running. During how many of this year’s physical education classes did Edgar have to run?

6. Find each product.

5 __6 of 6

3 __ 7 of 49

2 __ 5 of 20

1 ___ 10

of 70

6 __ 9 3 18

4 __5 3 45

5 ___12

3 36

8 __9 3 90

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Practice

11-4Multiplying Two FractionsWrite the multiplication problem that each model represents then solve. Put your answer in simplest form.

1. 2.

Find each product. Simplify if possible.

3. 7 __ 8 3 4 __

5 5

4. 3 __

7 3 2 __

3 5

5. 1 __ 6 3 2 __

5 5

6. 2 __

7 3 1 __

4 5

7. 2 __ 9 3 1 __

2 5

8. 3 __

4 3 1 __

3 5

9. 3 __ 8 3 4 __

9 5

10. 1 __

5 3 5 __

6 5

11. 2 __ 3 3 5 __

6 3 14 5

12. 1 __

2 3 1 __

3 3 1 __

4 5

13. If 4 _ 5 3j 5 2 _ 5 , what is j?

14. In Mrs. Marshall’s classroom, 6 _ 7 of the students play sports.Of the students who play sports, 4 _ 5 also play an instrument. If there are 35 students in her class, how many play sports and an instrument?

15. Which does the model represent?

A 3 _ 8 3 3 _ 5 C 3 _ 5 3 5 _ 8

B 7 _ 8 3 2 _ 5 D 4 _ 8 3 3 _ 5

16. Describe a model that represents 3 _ 3 3 4 _ 4

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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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1. The Lakeview School Environmental Club decided to plant a garden in the field behind their school building. They set up a rectangle that was 20.5 meters by 15.8 meters. What is the difference between the length and width of the garden?

A 5.7 m

B 5.3 m

C 5.0 m

D 4.7 m

2. Which of these drawings models 0.03?

A

B

C

D

3. What is the perimeter of a rectangle with sides of lengths 3 _ 4 inch and 2 _ 3 inch?

A 1 _ 2 in.

B 5 _ 7 in.

C 1 5 __ 12 in.

D 2 5 _ 6 in.

4. Write 3 fractions equivalent to 2 _ 3 .

5. Use order of operations to evaluate.

24 + 20 ÷ 4 – (3 × 2)

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Practice

11-5Area of a RectangleFind each area.

1. a rectangle with sides of lengths 4 _ 5 foot and 1 _ 2 foot

2. a rectangle with sides of lengths 1 _ 3 yard and 3 _ 4 yard

3. a rectangle with sides of lengths 2 _ 3 foot and 1 _ 3 foot

4. a rectangle with sides of lengths 5 _ 6 inch and 1 _ 3 inch

5. a square with sides of length 5 _ 8 inch

6. a rectangle with a length of 3 inches and a width of 1 _ 8 inch

7. a rectangle with a length of 1 _ 5 yard and a width of 2 _ 3 yard

8. a rectangle with a length of 4 _ 9 foot and a width of 2 feet

9. Mrs. Henley built a cage for her bird. She wanted to cover the bottom of the cage with newspaper. If the cage is 1 _ 4 yard by 1 _ 2 yard, what is the area that needs to be covered?

A 1 _ 8 sq. yd B 1 _ 4 sq. yd C 1 _ 2 sq. yd D 8 sq. yd

10. Writing to Explain Tariq and Marie each multiplied 1 _ 8 inch × 5 _ 8 inch. Tariq got 5 _ 8 sq. in. and Marie got 5 __ 64 sq. in. Which student found the correct area? How do you know?

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Quick Check

11-5

1. What is the area of a rectangle with a length of 6 inches and a height of 1 __ 12 inch?

A 1 _ 2 sq. in.

B 1 _ 4 sq. in.

C 5 __ 12 sq. in.

D 3 sq. in.

2. Find the area of a square with sides of length 1 _ 3 yard.

A 1 _ 3 sq. yd.

B 1 _ 4 sq. yd.

C 1 _ 9 sq. yd.

D 2 _ 9 sq. yd.

3. WritingtoExplain Yvonne wants to cover the back of her cellular phone with a colorful skin. If the phone’s length is 1 _ 3 foot and the phone’s width is 1 _ 6 foot, explain how to find the area that the skin will cover.

Q 11•5

431 2

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1. Find the product in simplest form:

3 __ 5 3 4 __

7 .

A 7 ___ 35

B 12 ___ 35

C 12 ___ 30

D 7 ___ 12

2. There is 5 _ 8 of a pie left over from last night. Jude eats 2 __ 15 of the leftover pie as a midnight snack. How much of the whole pie does Jude eat? Simplify your answer if possible.

A 5 ___ 12

B 2 ___ 15

C 5 ___ 60

D 1 ___ 12

3. On the number line, Z 5 ?

A 2 1 _ 4

B 2 1 _ 2

C 2 3 _ 4

D 3 1 _ 2

4. In Carolina’s class, 6 __16 of the children have freckles. Of the children with freckles, 1 __12 have red hair. What fraction of Carolina’s class has red hair and freckles? Simplify your answer, if possible.

5. There are 32 children in Carolina’s class. How many have both red hair and freckles?

6. Find each product. Simplify your answers, if possible.

6 __8 32 __

7

2 __ 3 31 __

4 35 __

6

9 ___ 12

34 __9

3 ___ 10

32 __5 34

7 ___ 16

38 ___14

5 ___ 16

34 ___15

33

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Practice

11-6Multiplying Mixed NumbersEstimate the product. Then complete the multiplication.

1. 5 4 _ 5 3 7 5 ______ 5 3 7 __

1 5 2. 3 2 _ 3 3 5 1 _ 7 5 ______

3 3 ______

7 5

Estimate. Then find each product. Simplify.

3. 4 3 _ 5 3 2 _ 3

5. 7 4 _ 5 3 2 1 _ 3

7. 2 1 _ 5 3 7 _ 8

9. 1 4 _ 5 3 1 1 _ 3 3 1 3 _ 4

4. 6 3 2 2 _ 7

6. 3 3 _ 4 3 2 4 _ 5

8. 6 1 _ 3 3 1 5 _ 6

10. 3 _ 4 3 2 2 _ 3 3 5 1 _ 5

11. Write a mixed number for p so that 3 1 _ 4 3 p is more than 3 1 _ 4 .

12. A model house is built on a base that measures 9 1 _ 4 in. wide and 8 4 _ 5 in. long. What is the total area of the model house’s base?

13. Which is 1 3 _ 4 of 150 1 _ 2 ?

A 263 B 263 1 _ 8 C 263 3 _ 8 D 264 3 _ 8

14. Megan’s dog Sparky eats 4 1 _ 4 cups of food each day. Explain how Megan can determine how much food to give Sparky if she needs to feed him only 2 _ 3 as much. Solve the problem.

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Quick Check

11-6

1. Find the product: 1 1 _ 4 3 5 3 _ 5 .

A 5 3 __ 20

B 6

C 6 1 _ 4

D 7

2. Find the product: 2 1 _ 8 3 1 1 _ 6 3 3.

A 8 3 __ 16

B 7 7 __ 16

C 6 7 __ 16

D 6 1 __ 48

3. A full bag of dog food weighs 5 1 _ 2 pounds. How much dog food do you have if there are 3 3 _ 4 bags in the cupboard?

A 22 3 _ 8 pounds

B 21 1 _ 4 pounds

C 20 5 _ 8 pounds

D 15 3 _ 8 pounds

4. WritingtoExplain Leanne walks at an average speed of 3 1 _ 3 miles per hour. How far does she walk in 2 hours, 15 minutes? Simplify fractions if possible. Show your work.

Q 11•6

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1. A newspaper headline states that a sinkhole is about 4 feet deep. Which could be the actual depth of the sinkhole?

A 64 in.

B 58 in.

C 42 in.

D 36 in.

2. Ms. Perry pays $340 per month to lease her car. How much will she pay to lease her car for two years?

A $680

B $4,080

C $6,080

D $8,160

3. What is the prime factorization of 54?

4. Solve x 1 8 5 34.

5. Draw the next three figures in this pattern.

6. Find 11 __ 12 2 2 _ 3 . Write the difference in simplest form.

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Practice

11-7Problem Solving: Multiple-Step ProblemsWrite and answer the hidden question(s) in each problem. Then solve the problem.

1. Rahm spent 2 1 _ 2 hours writing an essay. It took him 4 times as long to finish his science project. How long did it take Rahm to write the essay and finish the science project?

Hidden question(s):

Solution:

2. Lauren bought 20 ounces of sliced ham. She used 3 _ 4 of the ham to make sandwiches for her friends and 1 _ 5 of the ham in an omelet. How many ounces of ham were left?

Hidden question(s):

Solution:

3. Sarah cut off 1 _ 8 of a 48-inch piece of ribbon. Jane cut off 1 _ 9 of a 36-inch piece of ribbon. They compared their cut pieces. Whose piece is longer? How much longer?

Hidden question(s):

Solution:

4. Misty bought 3 CDs. The country music CD cost $12. The rock music CD cost 2 _ 3 as much as the country music CD. The platinum edition CD cost twice as much as the rock CD. What was the cost of the three CDs?

Hidden question(s):

Solution:

5. Choose one of the problems above. Explain how you determined the hidden question and why it was necessary to answer that question in order to solve the problem.

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Quick Check

11-7

1. Which is the hidden question in this problem?

Jason bought 6 season tickets to the theatre. Each ticket cost $120. A season parking pass cost $30. How much did Jason spend for the tickets and the parking pass?

A Will the tickets cost more than $1,500?

B How much more is the cost of the tickets than the cost of the parking pass?

C How much do six season tickets cost?

D How much will two parking passes cost?

2. At Kira’s school, 5 _ 9 of the 360 students bring their lunch. The other students buy lunch in the cafeteria. How many more students bring lunch from home than buy lunch?

A 280 more students

B 150 more students

C 80 more students

D 40 more students

3. Jeff had $20. He spent 1 _ 8 of his money on lunch and 2 _ 5 of his money at the movies. How much money does Jeff have left?

A $5.50

B $7.00

C $8.25

D $9.50

4. WritingtoExplain Write and answer the hidden questions for the problem below, and then solve the problem.

• In Wing A of a kennel, 5 _ 8 of the 24 dogs are male. In Wing B, 4 _ 5 of the 30 dogs are male. How many male dogs are in the two wings of the kennel?

Would you need to answer a hidden question to find how many dogs are in the two wings? Why or why not?

Q 11•7

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1. �Laurin�writes�the�number�pattern�below.�Which�is�the�rule�for�her�pattern?�1,� 5,� 9,�13,�17�…

A Add�4.

B Multiply�by�4.

C Subtract�4.

D Add�7,�Subtract�4.

2. �A�package�of�10�pens�costs�$5.�Ms.�Jackson�spent�$45�on�pens�for�her�office.�How�many�pens�did�she�buy?

A 9�pens

B 50�pens

C 90�pens

D 450�pens

3. �Liam�has�some�dimes�and�quarters.�He�has�7�more�quarters�than�he�has�dimes.�If�Liam�has�15�coins�in�all,�which�is�the�value�of�his�coins?

A $3.15

B $2.55

C $2.10

D $1.75

4. �Write�the�prime�factorization�for�24.�

5. Solve�3x�=�45.�

6. Circle�the�greater�number.

1,004,050,010

1�3�109�1�4�3�106�1�5�3�104�1�1

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Practice

11-8Fractions and DivisionWrite a division expression for each fraction.

1. 2 _ 9 2. 1 _ 7 3. 7 __ 10

4. 3 _ 4 5. 7 _ 8 6. 3 __ 16

7. 6 __ 13 8. 18 __ 23 9. 11 __ 12

Write each division expression as a fraction.

10. 3 4 8 11. 34 16 12. 6 4 11

13. 2 4 7 14. 4 4 10 15. 5 4 17

16. 4 4 9 17. 13 4 23 18. 17 4 100

19. Which term is any number that can be shown as the quotient of two integers?

A Rational number

B Prime number

C Decimal number

D Compatible number

20. Steve wanted to equally divide two sticks of butter among three bowls. Which fraction represents the amount of butter in each bowl?

A 5 _ 2

B 2 _ 3

C 3 _ 2

D 3 _ 6

21. Can the division expression 4 4 15 be shown as a fraction? If yes, write the fraction. Explain why or why not.

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Quick Check

11-8

1. Which division expression is shown on the number line?

A 1 4 9

B 9 4 1

C 9 4 9

D 1 4 1

2. Which fraction can be written as 8 4 15?

A 23 __ 15

B 15 __ 8

C 8 __ 23

D 8 __ 15

3. Each person received 5 _ 6 of a block of clay when five same-size blocks were equally divided among six artists. Which division expression is shown by the fraction?

A 6 4 1 _ 5

B 5 4 1 _ 6

C 6 4 5

D 5 4 6

4. WritingtoExplain Draw a number line to help you write 3 4 4 as a fraction. Explain how the number line supports your answer.

10

Q 11•8

12 in.

16 in.


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Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5D 11•9

1. �There�are�12�dogs�in�a�puppy-training�class.�Ten�of�them�have�learned�to�sit.�What�fraction�of�the�dogs�have�learned�to�sit?�

A ��1�__�6��

B ��1�__�5��

C ��3�__�4��

D ��5�__�6��

2. Grace�buys�a�set�of�14�notebooks.�Each�notebook�has�85�pages.�What�is�the�total�number�of�pages�for�all�the�notebooks?�

A 1,190

B 1,170

C � �425

D � �340

3. �Anna,�Pedro,�and�Cara�own�a�shop.�They�agree�to�share�the�profit�equally.�If�the�profit�is�$5,902,�which�is�the�best�estimate�of�each�owner’s�share?�

A $2,000

B $3,000

C $5,000

D $6,000

4. �The�drawing�shows�a�shelf�from�a�corner�cabinet.

�What�is�the�area�of�the�shelf�in�square�inches?

5. �A�rectangular�rug�has�a�base�b�and�a�height�h,�with�a�perimeter�of�30�feet.�Both�b�and�h�are�whole�numbers�between�5�and�10�feet.�Fill�in�the�blanks�to�complete�this�sentence:

Theareaoftherugisatleast�

�butnotgreater�

than .

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Practice

11-9Fractions, Mixed Numbers, and Decimals as QuotientsWrite each quotient as a fraction or mixed number.

1. 15 4 10 2. 4 4 10

3. 12 4 20 4. 62 4 5

Write each quotient as a decimal.

5. 4 4 10 6. 19 4 5

7. 32 4 20 8. 75 4 6

Write each quotient as a fraction or mixed number, and also as a decimal.

9. 2 4 10 10. 37 4 2

11. 21 4 6 12. 75 4 10

13. Lawrence is making 10 gift baskets. The table shows the food he has bought for the baskets. If the food is divided evenly, how much of each type of food will he put in each basket? Complete the table. Give each answer as either a fraction or mixed number, and also as a decimal.

Type of Food Total Amount (in lb)

Amount per Basket (in lb)

Chocolate-covered raisins 4

Cherries 22

Toasted almonds 5

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Quick Check

11-9

1. Find the quotient of 13 4 4 as a fraction or mixed number.

A 3 1 _ 4

B 4 __ 13

C 1 4 __ 13

D 1 3 _ 4

2. Find the quotient of 26 4 10 as a decimal.

A 0.26

B 1.26

C 2.6

D 20.6

3. Which does NOT represent the quotient of 17 4 10?

A 1 7 __ 10

B 1 R7

C 10 __ 17

D 1.7

4. WritingtoExplain Explain how to solve this problem. Show your work.

Cherylhas a 14-foot pole. She wants to cut it into 4 equal-sized pieces to stake up her tomato plants. How long should she cut each piece? Give the answer as a decimal. Show your work.

Q 11•9

Name




13 _5 331 _ 8

A 5

B 3 3 __ 40

C 64 ____ 125

D 1 __ 5

2. During Primrose School’s annual Walk for Education, Reba walked around the track 5 5 _ 6 times. Holt walked around the track 1 3 _ 5 times the number of times Reba did. How many times did Holt walk around the track? Simplify your answer.

A 3 41 ___ 128

B 5 1 _ 8

C 9 1 _ 3

D 9 5 __ 16

3. 3 ___ 12

. ?

A 0.31

B 0.28

C 0.25

D 0.22

4. During the mayoral election, two debates were held between the candidates. The first debate lasted 1 2 _ 3 hours. The second one was 1 4 _ 5 times as long as the first one. How many hours long was the second debate? Estimate the product. Then find the actual product. Simplify if possible.

5. Estimate the product. Then find the actual product. Simplify if possible.

3 _5 35 1 _ 3

4 1 _ 4 38

24 _ 5 362 _ 7

16 _ 9 352 _ 3

33 _ 5 3101 _ 4

72 _ 9 39

(1 6 _ 7 2 3 _ 4 ) 3 7

11 _2 3 (45 _ 6 123 _ 8 )

D 11•10

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Practice

11-10Dividing Whole Numbers by Unit FractionsIn 1 and 2, use the picture to find each quotient.

1. How many thirds are in 1? 2. How many thirds are in 7?

In 3 and 4, draw a picture to find each quotient.

3. 3 4 1 __ 2 4. 4 4 1 __

8

In 5 and 6, use multiplication to find each quotient.

5. 6 4 1 __ 3 6. 5 4 1 ___

10

7. Julie bought 3 yards of cloth to make holiday napkin rings. If she needs 3 _ 4 of a yard to make each ring, how many rings can she make?

8. When you divide a whole number by a fraction with a numerator of 1, explain how you can find the quotient.

P 11•10

INCHES0 1 2 3 4 5 6

38

38

38

38

38

38

38

38

38

38

38

38

38

38

38

38

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Quick Check

11-10

1. Using the picture below, what is the value of 6 4 3 __ 8 ?

A 12 B 16 C 24 D 48

2. Find the quotient: 15 4 5 __ 6 .

A 24 B 20 C 18 D 1

3. Find the quotient: 5 4 1 __ 5 .

A 25 B 20 C 5 D 1

4. Joel is using a recipe to make cookies for a club bake sale. According to the recipe, he needs 2 _ 3 cup of sugar for each batch of cookies. He has 6 cups of sugar. How many batches of cookies can he make without buying more sugar?

A 3 batches

B 8 batches

C 9 batches

D 12 batches

5. WritingtoExplain. On a camping trip, people are divided into several groups. Each group needs to fill a 3-quart ( 3 __ 4 -gallon) jug with water for cooking and mixing drinks. If the water tank holds 12 gallons of water, how many groups can fill their jugs from the tank? Explain your answer and show your work.

Q 11•10

Name




3 _ 4 × 4 _ 7

A 7 __ 28

B 3 _ 7

C 12 __ 35

D 7 __ 11

2. Meg colored 3 _ 8 of the tiles for her art project. Max has colored 4 __ 15 of the tiles for his project. Solve 3 _ 8 − 4 __ 15 to find how much more Meg has colored than Max.

A 1 _ 7

B 2 __ 15

C 17 ___ 120

D 13 ___ 120

3. Which of the following fractions is notequivalent to the others?

A 24 __ 36

B 8 __ 12

C 12 __ 16

D 4 _ 6

Use the table for 4 and 5. The top row is the hours Margie works and the bottom row is the money she earns.

Hours 2 3 4 5Dollars 16 24 ? ?

4. How much does Margie earn if she works for 4 hours? 5 hours?

5. What is the mathematical relationship between the top and bottom row?

6. Find each product. Simplify your answers if possible.

1 _ 2 × 5 _ 7

2 _ 3 × 5 _ 6 × 3 _ 4

5 __ 16 × 2 __ 15 × 4

6 _ 8 × 8 __ 18

7 __ 16 × 4 _ 7

2 __ 10 × 4 _ 5 × 5

D 11•11

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Practice

11-11

17. Cameronandhisfamilywereeatingleftoverlasagna.Therewas1_2ofthelasagnaleft.Cameronhasonebrother,onesister,andtwoparents.Ifeveryonegetsthesamesizepiece,whatfractionoftheoriginallasagnadoeseachmemberofCameron’sfamilyreceive?

DividingUnitFractionsbyNon-ZeroWholeNumbersIn1-16,findthequotient.

1. 1_4÷4

3. 1_2÷2

5. 1_4÷5

7. 1_6÷4

9. 1_2÷3

11. 1_4÷2

13. 1_6÷5

15. 1_2÷4

2. 1_3÷2

4. 1_5÷4

6. 1_7÷7

8. 1_9÷6

10. 1_3÷5

12. 1_5÷7

14. 1_7÷6

16. 1_9÷5

P 11•11

Quick Check

11-11Name


1. Use the picture below to find the quotient.

1 _ 5 ÷ 3

2. Find the quotient.

1 _ 6 ÷ 7

3. WritingtoExplain Richard has 1 _ 2 of a pizza left. He is going to divide it among his 6 friends. What fraction of the original pizza did each of Richard’s friends receive? Draw a picture to explain your answer.

Q 11•11

Name



1.

44 1 __ 3 5 ?

A 4 _ 3

B 4

C 12

D 13

2. Brenna has a piece of fabric that is 12 1 _ 2 yards long. She wants to cut the fabric into 5 strips. How long will each strip be?

A 1 1 _ 2

B 2

C 2 1 _ 2

D 2 3 _ 4

3. Find the product. Simplify your answer if necessary.

21 __3 3 1 2 __

3 5 ?

A 1 1 _ 3

B 3 8 _ 9

C 4

D 11 2 _ 3

4. Preesha has 6 pizzas. If she divides each pizza into eighths, how many people can have 2 pieces of pizza each?

5. Ryan estimates that he uses 2 _ 3 cup of syrup each time he eats pancakes. How many times will he be able to eat pancakes without running out of syrup if he has a giant bottle of syrup that contains 48 cups?

If Ryan uses only 3 _ 8 cup syrup out of the giant bottle each time he eats pancakes, how many times will he be able to eat pancakes without running out of syrup?

D 11•12

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Practice

11-12Problem Solving: Draw a Picture and Write an EquationSolve each problem. Draw a picture to show the main idea for each problem. Then write an equation and solve it. Write the answer in a complete sentence.

1. Bobby has 3 times as many model spaceships as his friend Sylvester does. Bobby has 21 spaceships. How many model spaceships does Sylvester have?

2. Dan saved $463 over the 12 weeks of summer break. He saved $297 of it during the last 4 weeks. How much did he save during the first 8 weeks?

3. Use a separate sheet of paper to show the main idea for the following problem. Choose the answer that solves the problem correctly.

A box of peanut-butter crackers was divided evenly among 6 children. Each child got 9 crackers. How many crackers were in the box?

A 54 B 48 C 39 D 36

4. Why is it helpful to draw a picture when attempting to solve an equation?

P 11•12

14

2

w feet

w feet

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Quick Check

11-12

1. Mark knows that his yard is 2 1 _ 4 times as long as it is wide. Which equation shows the length, in feet, of the fence that goes all the way around the yard if Mark measures the width as w feet?

A Perimeter 5 3 1 _ 4 w feet

B Perimeter 5 5 1 _ 2 w feet

C Perimeter 5 6 1 _ 2 w feet

D Perimeter 5 9w feet

2. Lisa ate 1 _ 8 of a pizza. Josh ate 2 1 _ 2 times as much as Lisa. What fraction of the pizza did Josh eat?

A 1 _ 4

B 5 __ 16

C 7 __ 16

D 1 __ 2

3. WritingtoExplain A model of a boat is 1 3 _ 8 feet long. How long is the model of a ship that is three times as long, if the models are made to the same scale? Make a drawing to help you solve the problem, and then calculate the answer. Show your work.

Q 11•12

Documents

Topic 11 - Weebly€¦ · D The 34th traveler in line 2. Shannon says, “My apartment number is a prime number.” Which could be Shannon’s apartment number? A 115 B 273 C 317