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##### Equivalent Fractions, Decimals and Fractions

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**Fractions that represent the same value are equivalent**fractions. So are equivalent fractions. 12 24 48 Vocabulary = =**Example 1**Find two equivalent fractions for . 4 __ 6**3**__ 5 Example 2: Multiplying and Dividing to Find Equivalent Fractions Find the missing number that makes the fractions equivalent. ___ = 20**3**__ 9 Example 3 Find the missing number that makes the fraction equivalent. ___ = 27**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.**Example 4: Writing Fractions in Simplest Form**Write each fraction in simplest form. 20 ___ 48**7**___ 10 Example 5: Writing Fractions in Simplest Form Write the fraction in simplest form.**12**___ 16 Example 6 Write each fraction in simplest form. 12 ___ 16**1**1 3 1 1 __ __ __ __ __ 1 1 1 2 2 4 2 4 4 2 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 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 12 34 14**Example 7: Writing Decimals as Fractions or Mixed Numbers**Write each decimal as a fraction or mixed number. 0.67**Example 8: Writing Decimals as Fractions or Mixed Numbers**Write each decimal as a fraction or mixed number. 5.9**Example 9**Write each decimal as a fraction or mixed number. 3.07**3**____ 20 Example 10: Writing Fractions as Decimals Write each fraction or mixed number as a decimal.**1**__ 3 Example 11: Writing Fractions as Decimals Write each fraction or mixed number as a decimal. 6**Common Fractions and Equivalent Decimals**1 2 1 1 1 3 2 3 4 __ __ __ __ __ __ __ __ __ 5 3 4 3 2 4 5 5 5 0.2 0.25 0.3 0.4 0.5 0.6 0.6 0.75 0.8 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**Example 12: Comparing and Ordering Fractions and Decimals**Order the fractions and decimal from least to greatest. 3 7 __ __ , 0.8, 10 4**Example 13**Order the fractions and decimal from least to greatest. 3 __ 0.3, , 0.53 5