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.
- Convert to a simple fraction.
- Rewrite as a compound number.
- Add the following numbers and convert the answer to a simple fraction: .
- Multiply the following numbers and convert the answer to a simple fraction: .
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