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Simplifying Complex Fractions

A complex fraction is a fraction that contains other fractions.

Here are three examples of complex fractions.

There are two methods for simplifying complex fractions.

Procedure

To Simplify a Complex Fraction

Step 1 Write the numerator and denominator each as a single fraction.

Step 2 Rewrite the complex fraction using the division symbol, Ã·.

Step 3 Invert the second fraction and change Ã· to Â·.

Step 4 Multiply.

Example

Simplify:

Solution
Step 1 Write the numerator and denominator each as a single fraction. The numerator and denominator are already single fractions.
Step 2 Rewrite the fraction using Ã·.
Step 3 Invert the second fraction and change Ã· to Â·.
Step 4 Multiply.
Factor the numerators and denominators.
Cancel all pairs of common factors.
Multiply.
So, the result is .

Note

In , the numerator is and the denominator is .