Relate Decimals and Fractions · Practice Lesson 21 Relate Decimals and Fractions Unit 4 Practice and Problem Solving Unit 4 Number and Operations—Fractions 226 Lesson 21 Relate

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©Curriculum Associates, LLC Copying is not permitted.220 Lesson 21 Relate Decimals and Fractions

Solve.

3 Fill in the blanks with numbers and fractions to make true sentences.

a. 1 15

··· 100 5 55

··· 100

tenths 1 hundredths 5 55 hundredths.

b. 1 4

·· 10 5 55

··· 100

hundredths 1 tenths 5 55 hundredths.

c. 1 5 ··· 100 5

55 ··· 100


d. 1 25

··· 100 5 55

··· 100


Of the 100 students in the fourth grade, 70 students are girls.

4 Write a fraction in tenths and a fraction in hundredths to tell what fraction of the fourth-grade students are girls.

5 Write a fraction in tenths and a fraction in hundredths to tell what fraction of the fourth-grade students are boys.

220220 Lesson 21Lesson 21220

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M

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7 ··· 10 and 70 ···· 100

3 ··· 10 and 30 ···· 100

4 ··· 10

4 15

15 ···· 100

15 4

5 ··· 10

5 5

3 ··· 10

3 25

©Curriculum Associates, LLC Copying is not permitted. 219Lesson 21 Relate Decimals and Fractions

Name:

Prerequisite: Find Equivalent Fractions

Study the example showing how to identify equivalent fractions with denominators of 10 and 100. Then solve problems 1−5.

1 Write the fractions that the models below show.

2 Look at problem 1. Use multiplication to fi nd the equivalent fractions.

Example

Explain how 6 ·· 10 5 60

··· 100 .

Use multiplication to find equivalent fractions.

Use models to show equivalent fractions.

6 ·· 10 = 60 ··· 100

6 ·· 10 5 1 6 3 10 ······· 10 3 10 2 5

60 ··· 100

Relate Decimals and Fractions

Lesson 21

Vocabularyequivalent fractions two or more fractions

that name the same part

of a whole.

219219 Relate Decimals and Fractions Relate Decimals and Fractions 219

B

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4 ··· 10 5 1 4 3 10

······· 10 3 10 2 5 40

···· 100

4 ··· 10

40 ···· 100

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Solve.

4 What decimal is equivalent to 80 ··· 100 ? Shade the model

below to show the fraction and the decimal. Then

write the decimal.

80 ··· 100 5

5 Look at problem 4. Shade the model below to show an equivalent tenths fraction and decimal. Then write the fraction and decimal.

5

6 Use what you know about equivalent fractions to explain why 0.8 and 0.80 are equivalent.

7 Find the sum of 80 ··· 100 and 20 ··· 100 . Then use what you

know about equivalent fractions to explain why

0.8 1 0.2 5 1.

M


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Answers will vary. Possible explanation: 0.8 5 8

··· 10 and 0.80 5 80

···· 100 .

8 ··· 10 is equivalent to 80 ···· 100 because 8 ··· 10 3 10 ··· 10 5 80 ···· 100 . So, 0.8 5 0.80.

Answers will vary. Possible explanation: 80 ···· 100 1 20 ···· 100 5 100 ···· 100 5 1. Write 80 ···· 100 and 20 ···· 100 as

tenths fractions. 80 ···· 100 5 8 ··· 10 and 20 ···· 100 5 2 ··· 10 . 8 ··· 10 1 2 ··· 10 5 10 ··· 10 5 1. So, 0.8 1 0.2 5 1.

0.80

8 ··· 10 0.8


Name: Name: Name: Lesson 21

Name the Same Amount

Study the example showing ways to name the same amount as a fraction and a decimal. Then solve problems 1–7.

1 What decimal is equivalent to 3 ·· 10 ?

Fill in the place-value chart to show the decimal.

Ones • Tenths

•

2 What decimal is equivalent to 55 ··· 100 ?

Fill in the place-value chart to show the decimal.

Ones • Tenths Hundredths

•

3 Write a decimal equivalent to 75 ··· 100 .

3

Example

How do you write decimals The model The model

equivalent to 7 ·· 10 and 70 ··· 100 ? shows 7 ·· 10 . shows 70 ··· 100 .

A place-value chart shows the

value of 7 ·· 10 and 70 ··· 100 . Ones • Tenths Hundredths

0 • 7 0 7 ·· 10 5 0.7 70 ··· 100 5 0.70

Vocabularydecimal fraction (or decimal) a number

containing a decimal

point that separates a

whole from fractional

place values, such as

tenths and hundredths.

0.7 and 0.70 are decimals.


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0 3

0 5 5

0.75

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Solve.

5 Tell whether each number sentence is True or False.

a. 0.3 5 3 ··· 100 u True u False

b. 0.03 5 3 ··· 100 u True u False

c. 0.3 5 30

··· 100 u True u False

d. 0.3 5 3

·· 10 u True u False

6 Write two equivalent fractions to 0.3.

7 Which of the following names the same number as 0.62? Circle the letter for all that apply.

A sixty-two hundredths

B six tenths and 2 hundredths

C 62 ·· 10

D 62 ··· 100

8 The number line below shows 1 whole divided into tenths. Write numbers in the boxes to label the missing fractions and decimal. Explain how you know what numbers to write.

0

0.1 0.2 0.4 0.5

1110

M


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M 3 ··· 10 and 30 ···· 100

Answers will vary. Possible explanation: 0.2 is two tenths or the fraction 2 ··· 10 .

0.4 is fourth tenths or the fraction 4 ··· 10 . 0.5 is five tenths or the fraction 5 ··· 10 .

I counted up by tenths from five tenths to get to eight tenths. Eight tenths

is the fraction 8 ··· 10 , or 0.8.

3333

0

0.1 0.2 0.4 0.5 0.8

1110

210

410

510

810


Name: Name: Name: Lesson 21

Write a Decimal as an Equivalent Fraction

Study the example problem showing how to write a decimal as an equivalent fraction. Then solve problems 1−8.

1 Shade the model below to show 0.34.

2 Show 0.34 in a place-value chart.

Ones • Tenths Hundredths

•

3 Write 0.34 in words.

4 Write 0.34 as a fraction.

Example

Alanna has an assortment of books in her bookcase. 0.09 of her books are comic books. What fraction of the books are comic books?

Decimal: 0.09

Words: 9 hundredths

Fraction: 9 ··· 100

9 ··· 100 of the books are comic books. Ones • Tenths Hundredths

0 • 0 9


M

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B

B

thirty-four hundredths

0 3 4

34 ···· 100

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5 Mackenzie has 1 dollar, 2 dimes, and 3 pennies. Jorge has only dimes and pennies but has the same amount of money as Mackenzie. How many dimes and pennies could Jorge have?

Show your work.

Solution:

Solve.

3 Austin bought an eraser for 65 cents and a pencil for 20 cents. What fraction of a dollar did he spend? Write the fraction as a decimal.

Show your work.

Solution:

4 Tell whether each number below is equivalent

to 15 ··· 100 .

a. fifteen hundredths u Yes u No

b. 1.5 u Yes u No

c. 15 ·· 10 u Yes u No

d. 0.15 u Yes u No

What fraction of a dollar is 1 cent?

How do you write this fraction in words and as a decimal?

Can you represent the value of a dollar, a dime, and a penny as fractions or decimals to help you solve this problem?


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Austin spent 85 ···· 100 or 0.85 of a dollar.

65 ···· 100 1

20 ···· 100 5

85 ···· 100

85 ···· 100 5 0.85 or 85 cents

Answers may vary. Possible work:

Mackenzie: 1 1 0.2 1 0.03

1 1 2

··· 10 1 3 ···· 100 5 1 23 ···· 100

Any combination of dimes and pennies that equals $1.23 is

acceptable. Possible answer: Jorge could have 12 dimes and 3 pennies.

Students might also draw a hundredths model and a tenths model to solve the problem.

3

3

33


Name:

2 Rita correctly answered 9 questions out of 10 on a test. What fraction of the test questions did Rita answer incorrectly?

A 9 ·· 10

B 9 ··· 100

C 1 ·· 10

D 1 ··· 100

Patrick chose A as the correct answer. How did he get that answer?

1 What is 0.5 written as a fraction?Circle the letter for all that apply.

A 5 ··· 100

B 5 ·· 10

C 50 ··· 100

D 50 ·· 10

Name: Name: Lesson 21

How can you say the decimal in words?

What fraction represents all the questions?

Relate Decimals and Fractions

Solve the problems.


M

B

Possible answer: Patrick found the fraction of

the questions that Rita answered correctly, 9 ··· 10 ,

instead of the fraction of questions that she

answered incorrectly, 1 ··· 10 .

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Relate Decimals and Fractions · Practice Lesson 21 Relate Decimals and Fractions Unit 4 Practice and Problem Solving Unit 4 Number and Operations—Fractions 226 Lesson 21 Relate