Subtract Fractions with Unlike Denominators

The algorithm for subtracting one fraction from another when they have unlike denominators is very similar to the algorithm for adding fractions with unlike denominators.

Algorithm for Subtracting Fractions with Unlike Denominators

1. Multiply both numerator and denominator of each fraction by the denominator of the other fraction. The resulting equivalent fractions will have the same denominator.

2. Subtract the equivalent fractions by subtracting the numerators and retaining the like denominator.

Example 1

What is the value of ?

Solution

Step 1 Multiply both the numerator and denominator of by 5, and multiply both the numerator and denominator of by 3.

Step 2 Replace each original fraction with its equivalent fraction. Subtract the equivalent fractions by subtracting numerators and retaining the denominator.

Example 2

Find .

Solution

Step 1

Step 2

We have discussed procedures for adding and subtracting fractions, as well as the reasoning behind them. It is very important to keep the reasoning in mind, since it may allow you to interpret practical problems correctly, as well as to recall the procedures.

One particularly common error can be avoided by keeping the meaning of the fractions in mind. When adding fractions, some students make the mistake of adding denominators as well as numerators. For example, By recognizing that each of the fractions being added is greater than , you may see that an answer less than 1 is unreasonable.