1Cademy - Simplifying $$\frac{\frac{1}{3}+\frac{1}{6}}{\frac{1}{2}-\frac{1}{3}}$$ by Writing it as Division

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Procedure to Simplify a Complex Rational Expression by Writing it as Division

Example

Simplifying $\frac{\frac{1}{3}+\frac{1}{6}}{\frac{1}{2}-\frac{1}{3}}$ by Writing it as Division

Simplify the complex rational expression $\frac{\frac{1}{3}+\frac{1}{6}}{\frac{1}{2}-\frac{1}{3}}$ by writing it as division:

Step 1. Simplify the numerator and denominator. Rewrite the fractions in the numerator with the common denominator 6: $\frac{1}{3} = \frac{2}{6}$ . Add: $\frac{2}{6} + \frac{1}{6} = \frac{3}{6}$ . Rewrite the fractions in the denominator with the common denominator 6: $\frac{1}{2} = \frac{3}{6}$ and $\frac{1}{3} = \frac{2}{6}$ . Subtract: $\frac{3}{6} - \frac{2}{6} = \frac{1}{6}$ .

Step 2. Rewrite the complex rational expression as a division problem. $\frac{3}{6} \div \frac{1}{6}$

Step 3. Divide the expressions. Multiply the first fraction by the reciprocal of the second: $\frac{3}{6} \cdot \frac{6}{1}$ Divide out the common factor of 6.

The result is 3.

Updated 2026-06-24

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OpenStax Elementary Algebra

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