Rule 27: Compound Fractions

A compound fraction is sometimes called a mixed number. Recall that , , and are examples of compound fractions.

• To manipulate compound fractions, just convert them to simple fractions and follow rules 1 through 23 for simple fractions.

  Example 1: Convert to a simple fraction.
  Answer. can be written . Write 3 as the fraction . Now can be written and

  

• To convert a simple fraction to a compound fraction, the numerator must be larger than the denominator. Separate the whole number first.

  Example 2: Convert to a compound fraction.

  Answer. Rewrite as . We have

  

• To add or subtract two compound fractions, convert the fractions to simple fractions and follow the steps you use to add or subtract two simple fractions.

  Example 3: Calculate .

  Solution We have

  

• To multiply or divide two compound fractions, convert the fractions to simple fractions and follow the steps you use to multiply or divide two simple fractions.

  Example 4: Calculate .

  Solution. We have

  

If you would like to review more examples, click on Example.

Work the following problems and click on Answer if you would like to check your answer and/or review the solution.

Problem 1:

Convert to a simple fraction.

Answer

Problem 2:

Rewrite as a compound number.

Answer

Problem 3:

Add the following numbers and convert the answer to a simple fraction: .

Answer

Problem 4:

Multiply the following numbers and convert the answer to a simple fraction: .

Answer

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