Name Practice 10-1 Using Models to Compare Fractions: Same Denominator · 2011-12-19 · 9. Two...

$Page 1: Name Practice 10-1 Using Models to Compare Fractions: Same Denominator · 2011-12-19 · 9. Two fractions have the same denominator. Which is the greater fraction: the fraction with$
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3P 10•1

Using Models to Compare Fractions: Same DenominatorCompare. Write >, <, or =.

1. 2.

3 __ 6 2 __

6 1 __

3 2 __

3

3. 2 __ 4 3 __

4 4. 5 __

6 3 __

6

5. 4 __ 6 1 __

6 6. 3 __

8 6 __

8

7. Why is 6 __ 8 greater than 5 __

8 but less

than 7 __ 8 ?

8. Reasonableness Marty ate

4 __ 6 of his pizza and Luis ate 5 __

6 of his

pizza. Marty ate more pizza than

Luis. How is that possible?

9. Two fractions have the same denominator. Which is the

greater fraction: the fraction with the greater numerator

or the lesser numerator?

10. Which is the greatest fraction?

A 0 __ 4 B 1 __

4 C 3 __

4 D 2 __

4

Practice

10-1

Name

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3P 10•2

Using Models to Compare Fractions: Same Numerator

Compare. Write <, >, or = for each .

1. 2.

1 __ 8 1 __

3 2 __

3 2 __

6

3. 3 __ 6 3 __

4 4. 1 __

2 1 __

2

5. 2 __ 8 2 __

6 6. 3 __

8 3 __

4

7. Ricardo has read 2 __ 3 of a book. Lin

had read 2 __ 4 of the same book. Who

has read more of the book?

8. Maria and Nina each ordered a

small pizza. Maria ate 3 __ 8 of her

pizza. Nina ate 3 __ 6 of her pizza. Who

ate more pizza?

9. Which is the greatest fraction?

A 1 __ 2 B 1 __

4 C 1 __

6 D 1 __

8

10. Writing to Explain Why is 1 __ 6 greater than 1 __

8 but less than 1 __

3 ?

Explain.

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10-2

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Comparing Fractions Using BenchmarksFor 1–9, use benchmark numbers to compare. Write < or > for each .

1. 3 __ 6 3 __

8 2. 2 __

3 1 __

3 3. 4 __

8 6 __

8

4. 2 __ 4 2 __

6 5. 1 __

4 1 __

3 6. 3 __

4

1 __

4

7. 3 __ 3 3 __

4 8. 5 __

8 5 __

6 9. 2 __

6 2 __

3

10. Explain how you compared the fractions in Exercise 9.

11. Which fraction is closer to 1 than to 0?

A 1 __ 4 B 1 __

2 C 3 __

6 D 7 __

8

12. Lucy has a collection of buttons. 2 __ 3 of her buttons are square and 2 __

8 of her

buttons are round. Does Lucy have more square buttons or round buttons?

13. Reason On Monday, Carlos ran 1 __ 8 of a mile. On Wednesday, he ran 5 __

6 of a mile.

Carlos ran 3 __ 8 of a mile on Friday. Which day did Carlos run the farthest?

14. Writing to Explain Sydney says that 4 __ 8 is closer to 0 than to 1. Is she

correct? Explain.

Practice

10-3

Name


Comparing Fractions on the Number Line

In 1–3, compare. Write ,, ., or 5.

Draw number lines to help.

1. 3 __ 4 1 __

4 2. 2 __

3 1 __

3 3. 6 __

8 7__

8

In 4–6, compare. Write ,, ., or 5.

Draw number lines to help.

4. 1 __ 2 1 __

4 5. 2 __

3 2 __

4 6. 1 __

4 1__

8

8. Reason Explain how you can use a number line to show that 5 __ 8 is

greater than 3 __ 8 .

7. Use Structure When do you need to use two number lines to compare

two fractions?

A When you compare fractions that have the same denominators.

B When you compare fractions that have different denominators.

C When you compare fractions that are greater than 1.

D When you compare fractions that refer to different wholes.

Practice

10-4

Name


Finding Equivalent FractionsComplete each number sentence.

1. 2. 3.

1 __ 4 � _____

8 3 __

4 � _____

8 3 __

6 � _____

4

Find the simplest form of each fraction.

4. 3 __ 6

5. 4 __ 6

6. 3 __ 8

Name a fraction to solve each problem.

7. Rob colored 1 __ 4 of a rectangle. What

is another way to name 1 __ 4 ?

9. Use Tools When using fraction

strips, how do you know that two

fractions are equivalent?

8. Three eighths of the cast in a

musical have to sing. What

fraction of the cast does not have

to sing?

10. Samuel has read 3 __ 6 of his

assignment. Judy has read 4 __ 8 of

her assignment. Their assignments

were the same size. Which

sentence is true?

A Samuel read more than Judy.

B Judy read more than Samuel.

C They read the same amount.

D They will both finish the

assignment at the same time.

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Equivalent Fractions and the Number Line

1. Write two fractions that name the location on the number line below.

For 2 and 3, draw a number line to show that the fractions are equivalent.

2. 3 __ 4 � 6 __

8 3. 1 __

4 � 2 __

8

4. Reason Explain how you can use a number line to show that 3 _ 6 and 1 _

2 are

equivalent fractions.

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Practice

10-6

Practice

10-7Name

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 3

Whole Numbers and Fractions

In 1–6, write an equivalent fraction for each whole number.

1. 6

2. 8

3. 4

4. 3

5. 1

6. 5

7. Reason Explain how you know 6 __ 6 and 1 are equivalent.

In 8–9, complete each number line.

8. thirds

9. fourths

10. Which whole number is equivalent to 8 __ 2 ?

A 2 B 4 C 6 D 8

11. Critique Reasoning Molly is wrapping up parts of sandwiches to sell at her sandwich cart. She cuts each sandwich in fourths and then wraps each fourth separately. She says that she wrapped 16 fourths, so she wrapped 16 whole sandwiches. What was Molly’s mistake?

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Fruit Salad

1 cups apples

1 batch

12

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1 cups grapes34_

1 cups cherries24_

2 cups bananas24_

2 cups pineapple14_

cup raisins_

cup coconut34_

Name


Using FractionsIn 1–6, compare. Write <, >, or =.

1. 6 __ 8 1 __

2 2. 2 __

4 3 __

6 3. 2 __

8 2 __

6

4. 1 __ 2 2 __

6 5. 3 __

4 3 __

8 6. 1 __

4 3 __

8

7. Complete the number line by writing the

missing fractions and mixed numbers.

8. About how much of this glass is

filled?

A 1 __ 3

B 3 __ 4

C 1 __ 2

D 1 __ 8

9. Which fraction describes the part

of this blanket that is white?

A 2 __ 3

B 1 __ 2

C 2 __ 4

D 2 __ 8

In 10–13, name the fruit with the greater number

of cups in the recipe at the right.

10. Apples or bananas?

11. Grapes or coconut?

12. Raisins or cherries?

13. Apples or pineapple?

14. One batch of fruit salad has equal amounts of which

kinds of fruit? Explain how you decided.

Practice

10-8

Name


Problem Solving: Draw a PictureSolve. Draw a picture.

1. Larry used a pattern of colors to make a cube train. He used

a red cube, a blue cube, a red cube, and another red cube

before he started the pattern again. He used 15 cubes.

How many red cubes did Larry use?

2. Two pizzas were each cut into sixths. Ashraf, Drew,

and Katie shared the pizzas equally. How many

sixths did each friend get?

3. Eric and Frank want to equally share 4 __ 3 feet of rope. What

length of rope should each friend get? Explain how to use a

drawing to help solve the problem.

4. A square garden is 12 feet long on each side. Janet needs to

put a post at each corner. She also needs to put a post every

3 feet on each side. How many posts does Janet need?

A 12 B 16 C 20 D 24

Practice

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Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 31 of 3Topic 10

1. Fabian used fraction strips to compare fractions. Which comparison is true? (10-2)

A 2 __ 3 > 2 __ 6

B 2 __ 6 > 2 __ 4

C 2 __ 3 < 2 __ 6

D 2 __ 3 < 2 __ 4

2. Tina ran 2 __ 6 mile on Monday and 5 __ 6 mile on Tuesday. Use the number line to find which is the correct symbol to compare the fractions. (10-4)

2 __6 5 __ 6

A 5

B 3

C .

D ,

3. Derek jogged for 5 _ 6 of an hour. Mindy jogged for 4 _ 6 of an hour. Use the fraction strips to find which is the correct symbol to compare the fractions. (10-1)

5 __6 4 __ 6

A 5

B 3

C .

D ,

4. Which lists the fractions in order from least to greatest? (10-8)

A 1 __ 2 , 3 __ 4 , 3 __ 8

B 3 __ 8 , 1 __ 2 , 3 __ 4

C 3 __ 4 , 3 __ 8 , 1 __ 2

D 3 __ 4 , 1 __ 2 , 3 __ 8

Topic 10

Test

MTH12_ANC3_TRM_TT10.indd 1 8/18/11 3:57 AM

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5. Which number makes the sentence true? (10-5)

2 __4 5  __ 8

A 2

B 4

C 6

D 8

6. Sean swam 3 __ 8 of a mile on Monday. On Wednesday, he swam 3 __ 6 of a mile. He swam 3 __ 4 of a mile on Friday. On Sunday, he swam 2 __ 8 mile. Use benchmark numbers to find which day Sean swam the farthest. (10-3)

A Monday

B Wednesday

C Friday

D Sunday

7. Richard wants to know if two insects are the same length. One insect is 2 __ 8 inch long. The other is 1 __ 4 inch long. Draw a number line to show they are the same length. (10-6)

8. Four friends were building a wall. Matt built 3 __ 8 of the wall. Tim built 2 __ 8 of the wall. Pat completed 1 __ 8 of the wall. Lucy built 2 __ 8 of the wall. How much of the wall did they build? (10-7)

9. Pilar, Jeff, and Alex shared some waffles that were cut into fourths. Pilar ate 3 __ 4 waffle, Jeff ate 2 __ 4 waffle, and Alex ate 4 __ 4 waffle. Who ate the least? Explain. (10-8)

10. Tania is building a bookcase. The bookcase is 8 feet tall. Tania put a shelf at the bottom. Then she put a shelf every 2 feet above the bottom shelf. There is no shelf at the top of the bookcase. How many shelves does the bookcase have? Draw a picture to solve. (10-9)

8_8ofthewallorthewholewall.

4shelvesCheckstudents’drawings.

Jeff;Sampleanswer:Jeffate2_4waffle,whichisafractionlessthan3_4andalsolessthan4_4.

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11. Julie painted 2 __ 4 of the fence around her house. What are two other ways to name 2 __ 4 ? (10-5)

12. Every container of fruit salad contains 1 __ 3 of an apple. How many whole apples are there in 6 containers of fruit salad? (10-7)

13. The county built a new bike path. The bike path is 12 miles long. They put up mile markers at the start and end of the path, and for every mile in between. How many mile markers did they put up on the bike path? (10-9)

14. Ryan and Andie had the same number of softballs at the start of the season. Ryan gave away 3 __ 8 of his softballs. Andie gave away 2 __ 3 of her softballs. Who gave away more softballs, Ryan or Andie? Explain how you can tell using benchmark numbers. (10-3)

15. Ronald spent the day making a painting for his friend. At the end of the day, Ronald finished 1 __ 4 of the painting. If he is able to finish as much of a painting each day he works, how long will it take Ronald to make 2 whole paintings? (10-7)

16. Immanuel finished reading 3 __ 4 of a book for a summer reading project. Sanjay read 3 __ 6 of a book for the same project. Who read more of their book? (10-4)

17. Patrick ate 2 __ 3 of a fruit bar. Write an equivalent fraction for the amount of fruit bar Patrick ate? (10-6)

1_2;4_8

2apples

8days

Immanuel13milemarkers

Andiegaveaway more

softballs;2_3ismore than1_2and3_8islessthan1_2.

4_6

3 of 3Topic 10


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1. Fabian used fraction strips to compare fractions. Which comparison is true? (10-2)

A 2 __ 3 > 2 __ 6

B 2 __ 6 > 2 __ 4

C 2 __ 3 < 2 __ 6

D 2 __ 3 < 2 __ 4

2. Tina ran 2 __ 6 mile on Monday and 5 __ 6 mile on Tuesday. Use the number line to find which is the correct symbol to compare the fractions. (10-4)

2 __6 5 __ 6

A 5

B 3

C .

D ,

3. Derek jogged for 5 _ 6 of an hour. Mindy jogged for 4 _ 6 of an hour. Use the fraction strips to find which is the correct symbol to compare the fractions. (10-1)

5 __6 4 __ 6

A 5

B 3

C .

D ,

4. Which lists the fractions in order from least to greatest? (10-8)

A 1 __ 2 , 3 __ 4 , 3 __ 8

B 3 __ 8 , 1 __ 2 , 3 __ 4

C 3 __ 4 , 3 __ 8 , 1 __ 2

D 3 __ 4 , 1 __ 2 , 3 __ 8

Topic 10

Test

MTH12_ANC3_TRM_TT10.indd 1 8/18/11 3:57 AM

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5. Which number makes the sentence true? (10-5)

2 __4 5  __ 8

A 2

B 4

C 6

D 8

6. Sean swam 3 __ 8 of a mile on Monday. On Wednesday, he swam 3 __ 6 of a mile. He swam 3 __ 4 of a mile on Friday. On Sunday, he swam 2 __ 8 mile. Use benchmark numbers to find which day Sean swam the farthest. (10-3)

A Monday

B Wednesday

C Friday

D Sunday

7. Richard wants to know if two insects are the same length. One insect is 2 __ 8 inch long. The other is 1 __ 4 inch long. Draw a number line to show they are the same length. (10-6)

8. Four friends were building a wall. Matt built 3 __ 8 of the wall. Tim built 2 __ 8 of the wall. Pat completed 1 __ 8 of the wall. Lucy built 2 __ 8 of the wall. How much of the wall did they build? (10-7)

9. Pilar, Jeff, and Alex shared some waffles that were cut into fourths. Pilar ate 3 __ 4 waffle, Jeff ate 2 __ 4 waffle, and Alex ate 4 __ 4 waffle. Who ate the least? Explain. (10-8)

10. Tania is building a bookcase. The bookcase is 8 feet tall. Tania put a shelf at the bottom. Then she put a shelf every 2 feet above the bottom shelf. There is no shelf at the top of the bookcase. How many shelves does the bookcase have? Draw a picture to solve. (10-9)


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11. Julie painted 2 __ 4 of the fence around her house. What are two other ways to name 2 __ 4 ? (10-5)

12. Every container of fruit salad contains 1 __ 3 of an apple. How many whole apples are there in 6 containers of fruit salad? (10-7)

13. The county built a new bike path. The bike path is 12 miles long. They put up mile markers at the start and end of the path, and for every mile in between. How many mile markers did they put up on the bike path? (10-9)

14. Ryan and Andie had the same number of softballs at the start of the season. Ryan gave away 3 __ 8 of his softballs. Andie gave away 2 __ 3 of her softballs. Who gave away more softballs, Ryan or Andie? Explain how you can tell using benchmark numbers. (10-3)

15. Ronald spent the day making a painting for his friend. At the end of the day, Ronald finished 1 __ 4 of the painting. If he is able to finish as much of a painting each day he works, how long will it take Ronald to make 2 whole paintings? (10-7)

16. Immanuel finished reading 3 __ 4 of a book for a summer reading project. Sanjay read 3 __ 6 of a book for the same project. Who read more of their book? (10-4)

17. Patrick ate 2 __ 3 of a fruit bar. Write an equivalent fraction for the amount of fruit bar Patrick ate? (10-6)

3 of 3Topic 10


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Name Practice 10-1 Using Models to Compare Fractions: Same Denominator · 2011-12-19 · 9. Two...

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