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Understanding Equivalent Fractions: Decimals and Fractions

Explore how fractions and decimals represent the same values, finding equivalent fractions, simplifying fractions to simplest form, converting between decimals and fractions, and the concept of mixed numbers. Learn through examples and vocabulary.

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Understanding Equivalent Fractions: Decimals and Fractions

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  1. Equivalent Fractions, Decimals and Fractions #13

  2. Fractions that represent the same value are equivalent fractions. So are equivalent fractions. 12 24 48 Vocabulary = =

  3. Example 1 Find two equivalent fractions for . 4 __ 6

  4. 3 __ 5 Example 2: Multiplying and Dividing to Find Equivalent Fractions Find the missing number that makes the fractions equivalent. ___ = 20

  5. 3 __ 9 Example 3 Find the missing number that makes the fraction equivalent. ___ = 27

  6. 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.

  7. Example 4: Writing Fractions in Simplest Form Write each fraction in simplest form. 20 ___ 48

  8. 7 ___ 10 Example 5: Writing Fractions in Simplest Form Write the fraction in simplest form.

  9. 12 ___ 16 Example 6 Write each fraction in simplest form. 12 ___ 16

  10. 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

  11. Example 7: Writing Decimals as Fractions or Mixed Numbers Write each decimal as a fraction or mixed number. 0.67

  12. Example 8: Writing Decimals as Fractions or Mixed Numbers Write each decimal as a fraction or mixed number. 5.9

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

  14. 3 ____ 20 Example 10: Writing Fractions as Decimals Write each fraction or mixed number as a decimal.

  15. 1 __ 3 Example 11: Writing Fractions as Decimals Write each fraction or mixed number as a decimal. 6

  16. 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

  17. Example 12: Comparing and Ordering Fractions and Decimals Order the fractions and decimal from least to greatest. 3 7 __ __ , 0.8, 10 4

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

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