How to Subtract Fractions with Unlike Denominators

Answer: To subtract fractions with unlike denominators, find a common denominator, then subtract the numerators while keeping the common denominator unchanged.

When subtracting fractions with unlike denominators, follow these steps:

1. Find a Common Denominator: Identify the least common multiple (LCM) of the denominators of the fractions. This common denominator will allow you to perform the subtraction operation.
2. Convert Fractions: Rewrite each fraction with the common denominator. To do this, multiply the numerator and denominator of each fraction by the appropriate factor to make the denominators equal to the common denominator found in Step 1.
3. Subtract Numerators: Once the fractions have the same denominator, subtract the numerators while keeping the common denominator unchanged.
4. Simplify (if necessary): If the resulting fraction can be simplified, reduce it to its simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD).

For example, let’s subtract 1/4 from 2/3:

1. Find a Common Denominator: The least common multiple of 4 and 3 is 12.
2. Convert Fractions: Rewrite each fraction with the common denominator 12:
   • 2/3 becomes (2 * 4)/(3 * 4) = 8/12.
   • 1/4 becomes (1 * 3)/(4 * 3) = 3/12.
3. Subtract Numerators: Subtract the numerators while keeping the common denominator unchanged:
   • 8/12 – 3/12 = (8 – 3)/12 = 5/12.
4. Simplify (if necessary): The resulting fraction, 5/12, is already in simplest form.

So, the difference between 2/3 and 1/4 is 5/12.