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Key
B Basic M Medium C Challenge
©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
tenths 1 hundredths 5 55 hundredths.
d. 1 25
··· 100 5 55
··· 100
tenths 1 hundredths 5 55 hundredths.
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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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
B
4 ··· 10 5 1 4 3 10
······· 10 3 10 2 5 40
···· 100
4 ··· 10
40 ···· 100
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©Curriculum Associates, LLC Copying is not permitted.222 Lesson 21 Relate Decimals and Fractions
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
©Curriculum Associates, LLC Copying is not permitted. 221Lesson 21 Relate Decimals and Fractions
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.
221221 Relate Decimals and Fractions Relate Decimals and Fractions 221
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B
0 3
0 5 5
0.75
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©Curriculum Associates, LLC Copying is not permitted.224 Lesson 21 Relate Decimals and Fractions
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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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
©Curriculum Associates, LLC Copying is not permitted. 223Lesson 21 Relate Decimals and Fractions
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
223223 Relate Decimals and Fractions Relate Decimals and Fractions 223
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B
B
thirty-four hundredths
0 3 4
34 ···· 100
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©Curriculum Associates, LLC Copying is not permitted.226 Lesson 21 Relate Decimals and Fractions
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
©Curriculum Associates, LLC Copying is not permitted. 225Lesson 21 Relate Decimals and Fractions
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.
225225 Relate Decimals and Fractions Relate Decimals and Fractions 225
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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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