How to Add Fractions with Different Bottom Numbers?

To add fractions with different bottom numbers (denominators), you must first find a common denominator. Here's a step-by-step explanation:

1. Find the Least Common Multiple (LCM) of the denominators. The LCM is the smallest number that both denominators divide into evenly. This LCM will be your common denominator.

2. Convert each fraction to an equivalent fraction with the common denominator. To do this, divide the common denominator by the original denominator of each fraction. Then, multiply both the numerator and denominator of the original fraction by the result.

3. Add the numerators of the equivalent fractions. Keep the common denominator the same.

4. Simplify the resulting fraction, if possible.

Example:

Let's add 2/5 and 1/3.

1. Find the LCM of 5 and 3: The LCM of 5 and 3 is 15.

2. Convert the fractions:

   • For 2/5: Divide 15 by 5, which equals 3. Multiply both the numerator and denominator of 2/5 by 3: (2 3) / (5 3) = 6/15.
   • For 1/3: Divide 15 by 3, which equals 5. Multiply both the numerator and denominator of 1/3 by 5: (1 5) / (3 5) = 5/15.

3. Add the numerators: 6/15 + 5/15 = (6+5)/15 = 11/15

4. Simplify: 11/15 is already in its simplest form.

Therefore, 2/5 + 1/3 = 11/15.