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**Equivalent Fractions, Decimals and Fractions**

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Vocabulary Fractions that represent the same value are equivalent fractions. So are equivalent fractions. 1 2 2 4 4 8 = =

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**Find two equivalent fractions for .**

Example 1 Find two equivalent fractions for . 4 __ 6

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**Example 2: Multiplying and Dividing to Find Equivalent Fractions**

Find the missing number that makes the fractions equivalent. 3 5 __ ___ = 20

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**Find the missing number that makes the fraction equivalent.**

Example 3 Find the missing number that makes the fraction equivalent. 3 9 __ ___ = 27

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Vocabulary Every fraction has one equivalent fraction that is called the simplest form of the fraction. A fraction is in simplest form when the GCF of the numerator and the denominator is 1.

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**Example 4: Writing Fractions in Simplest Form**

Write each fraction in simplest form. 20 ___ 48

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**Example 5: Writing Fractions in Simplest Form**

Write the fraction in simplest form. 7 10 ___

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**Write each fraction in simplest form.**

Example 6 Write each fraction in simplest form. 12 ___ 16 12 16 ___

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Vocabulary A number that contains both a whole number greater than 0 and a fraction, such as 1 , is called a mixed number. __ 3 4 Mixed numbers 1 4 1 2 3 4 __ 4 1 1 __ 2 1 __ 4 3 2 __ 4 1 2 __ 1

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**Example 7: Writing Decimals as Fractions or Mixed Numbers**

Write each decimal as a fraction or mixed number. 0.67

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**Example 8: Writing Decimals as Fractions or Mixed Numbers**

Write each decimal as a fraction or mixed number. 5.9

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Example 9 Write each decimal as a fraction or mixed number. 3.07

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**Example 10: Writing Fractions as Decimals**

Write each fraction or mixed number as a decimal. 20 ____ 3

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**Example 11: Writing Fractions as Decimals**

Write each fraction or mixed number as a decimal. 3 __ 1 6

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**Common Fractions and Equivalent Decimals**

Vocabulary A terminating decimal, such as 0.75, has a finite number of decimal places. A repeating decimal, such as 0.666…, has a block of one or more digits that repeat continuously 0.8 0.75 0.6 0.5 0.4 0.3 0.25 0.2 Common Fractions and Equivalent Decimals 1 5 __ 1 4 __ 1 3 __ 2 5 __ 1 2 __ 3 5 __ 2 3 __ 3 4 __ 4 5 __

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**Example 12: Comparing and Ordering Fractions and Decimals**

Order the fractions and decimal from least to greatest. __ 3 __ 7 , 0.8, 4 10

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**Order the fractions and decimal from least to greatest.**

Example 13 Order the fractions and decimal from least to greatest. 3 0.3, __ , 0.53 5

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