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