Practice Lesson 17 Find Equivalent Fractions

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©Curriculum Associates, LLC Copying is not permitted.188 Lesson 17 Find Equivalent Fractions

Shade to show the fractions. Are the two fractions equivalent? Choose Yes or No.

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6 48

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7 Use the bars to show that 2 ·· 3 is not equivalent to 7 ·· 8 .

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Explain how your drawing shows that 2 ·· 3 and 7 ·· 8 are not equivalent.

u Yes u No

u Yes u No

u Yes u No

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Possible answer: I broke the first bar into 3 equal pieces and I shaded 2 of them.

Then I broke the other bar into 8 equal pieces and I shaded 7 of them. You can see

that the bottom bar has more shaded than the top bar. So, 2 ·· 3 and 7 ·· 8 are not

equivalent.

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©Curriculum Associates, LLC Copying is not permitted. 187Lesson 17 Find Equivalent Fractions

Name:

Vocabularyequivalent fractions fractions that name the

same number.

1 ·· 2 and 2 ·· 4 are equivalent.

Prerequisite: Identify Equivalent Fractions

Study the example showing how to decide if two fractions are equivalent. Then solve problems 1–7.

Shade the bars to show the equivalent fractions.

1

2

Write the equivalent fractions these bars show.

3

Example

The bars are the same size.

The parts are different sizes.

The same amount is shaded on each bar.

So, 1 ·· 2 5 3 ·· 6 .

1 ·· 2 and 3 ·· 6 are equivalent fractions.

Find Equivalent Fractions

Lesson 17

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Shade the bars to show equivalent fractions. Then fill in the blanks to write equivalent fractions.

4

1 ·· 2 5 8

5

2 ·· 3 5 6

Draw lines and shade to show equivalent fractions. Then fill in the blanks to write equivalent fractions.

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1 ·· 2 5 4

7

4 ·· 6 5 3

8 What is a fraction equivalent to 4 ·· 4 ? Explain how you know.

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Answers will vary. Possible answer: 2 ·· 2 ; If I shaded 4 ·· 4 of a shape, I would shade the

whole shape. If I shaded 2 ·· 2 of the same shape, I would also shade the whole shape.

4 ·· 4 and 2 ·· 2 are both equal to 1 whole, so 4 ·· 4 5 2 ·· 2 .

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Name: Lesson 17


Study the example showing how to find equivalent fractions. Then solve problems 1–8.

Use the number line to complete the equivalent fractions.

0 18

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0 1

1 1 ·· 4 5 8

2 6 ·· 8 5 4

3 2 ·· 4 5

Example

Maria colored 1 ·· 3 of her art paper red. Erica colored 2 ·· 6 of her art paper yellow. Did the two girls color the same amount of their art papers?

0 16

26

36

46

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0 113

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One third is equal to two sixths.

1 ·· 3 5 2 ·· 6

Both girls colored the same amount of their art papers.

Vocabularyequivalent fractions fractions that name the

same number.

1 ·· 2 and 2 ·· 4 are equivalent.

Maria colored 1 ·· 3

Erica colored 2 ·· 6

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or 1 ·· 2

2

3

4

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B

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Use this number line to answer problems 5–8.

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44

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0 1 2 3

5 1 5 4

6 2 5 4

7 3 5 4

8 0 5 4

Use this number line to answer problems 9–11.

0 1 2 3

9 One whole is equal to eighths.

10 16 eighths is equal to wholes.

11 3 5 8

12 Use the model below to write a fraction equivalent to 3.

3 5

13 Draw a model to show 2 5 8 ·· 4 .

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Students’ models will vary. They may draw number lines labeled with whole numbers and fourths. They may also draw 2 same-size shapes divided into 4 equal pieces, with all 4 pieces in each shape shaded.

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Name: Lesson 17

Write a Whole Number as a Fraction

Study the example showing different ways to write whole numbers as fractions. Then solve problems 1–13.

Write the whole numbers as fractions.

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1 1 5 3

2 2 5 3

3 3 5 3

4 4 5 3

Example

Mrs. Clark cut 2 same-size pieces of colored paper into sixths to make strips for paper chains. How many strips did she make?

1 whole 5 six 1 ·· 6 s

1 5 6 ·· 6

2 wholes 5 twelve 1 ·· 6 s

2 5 12 ·· 6

Mrs. Clark made 12 strips. Each strip is 1 ·· 6 of a whole piece of paper.

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Write the whole number for each fraction.

9 9 ·· 1 5 10 10 ·· 1 5

Write the fraction for each whole number.

11 12 5 12 18 5

13 Explain how to write a whole number as a fraction with a denominator of 1.

Vocabularynumerator the number

above the line in a

fraction; it tells how

many equal parts are

described.

denominator the

number below the line in

a fraction; it tells how

many equal parts are in

the whole.

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14 Bella says this model shows 3 wholes. She says it

shows that if you write the whole number 3 as a

fraction, you have to write 3 5 12 ·· 4 .

How can you explain to Bella that there are other ways to write 3 as a fraction?

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Possible answer: Write the whole number as the numerator of the fraction and

use 1 as the denominator.

Possible answer: I would tell her there are

different ways to write a whole number as a

fraction. The denominator could be 1 instead

of 4 if you don’t divide the whole into pieces.

So you could write 3 as 3 ·· 1 . You could also divide

each whole into different numbers of parts. If

you divided each whole into 2 parts, you

would get 3 5 6 ·· 2 .

18 ··· 1

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12 ··· 1

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Name:

Example

The spaces between whole numbers on this number line are not divided into smaller parts. So, each whole has only 1 part.

0 31

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41

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0 1 2 3 4 5 6

The number line shows that 3 ·· 1 is equal to 3.

3 ·· 1 is a fraction name for 3.

Write a Whole Number as a Fraction with a Denominator of 1

Study the example showing different ways to write a whole number as a fraction with a denominator of 1. Then solve problems 1–14.

Write the whole number for each fraction.

1 4 ·· 1 5 2 2 ·· 1 5

3 5 ·· 1 5 4 8 ·· 1 5

Write the fraction for each whole number.

5 2 5 6 5 5

7 1 5 8 7 5

Lesson 17

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7 ·· 1

5 ·· 1

1 ·· 1

2 ·· 1

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6 Which statements are true? Circle the letter of all that apply.

A 4 ·· 2 5 2 D 2 ·· 4 5 1 ·· 2

B 4 ·· 1 5 4 E 1 ·· 2 5 2 ·· 1

C 1 ·· 3 5 3

Solve.

4 Jeff ’s pizza is cut into 8 equal pieces. He eats 1 ·· 2 of it.

What fraction of the pizza does he eat?

A 2 ·· 8 C 4 ·· 8

B 8 ·· 8 D 3 ·· 8

Samantha chose A as the correct answer. How did she get that answer?

5 Draw lines and shade rectangles A and B to show that 1 ·· 4 5 2 ·· 8 .

A B

Explain your work.

How many eighths are equal to 1 · 2 ? How many fourths?

How many equal parts will you show in A? In B?

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Samantha may have used the denominator of 1 ·· 2 as the

numerator of the fraction. Then she used the number of

equal pieces as the denominator.

Possible answer: Both rectangles are the same

size. I made 4 equal pieces in A and shaded 1 to

show 1 ·· 4 . I made 8 equal pieces in B and shaded 2

to cover the same amount as A.

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Name:

3 Draw a model to show that 3 5 6 ·· 2 .

Explain your drawing.

2 Mrs. White is painting the fence in her yard. After

painting 4 ·· 6 of the fence she stops for lunch. Which

fraction is equivalent to 4 ·· 6 ?

A 1 ·· 3

B 3 ·· 2

C 2 ·· 6

D 2 ·· 3

1 Use the number line.

0 14

34

24

44

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Which fraction is equivalent to 6 ·· 4 ?

A 2 ·· 3 C 3 ·· 2

B 4 ·· 6 D 2


Solve the problems.

Lesson 17

Equivalent means “another name for.”

I see a way to divide the rectangle into equal parts that are bigger than sixths.

What does a model of two halves look like?

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Possible answer: One whole is the same as

2 halves. 2 1 2 1 2 5 6, so I drew 2 halves

3 times. That shows 3 wholes and 6 halves.

Practice Lesson 17 Find Equivalent Fractions

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