How to Add Fractions?

Adding fractions comes down to one rule: you can only add fractions that have the same (common) denominator. Once the bottoms match, you just add the tops.

Case 1 — Same denominator (easy):

Add the numerators (top numbers) and keep the denominator (bottom number) the same.

• Example: 1/5 + 2/5 = 3/5

Case 2 — Different denominators:

You first need a common denominator.

1. Find a common denominator. Use the least common multiple of the two denominators (or just multiply them together).
2. Convert each fraction to an equivalent fraction with that denominator by multiplying the top and bottom by the same number.
3. Add the numerators, keep the common denominator.
4. Simplify the result if possible.

Worked example: 1/2 + 1/3

• Common denominator of 2 and 3 is 6.
• Convert: 1/2 = 3/6, and 1/3 = 2/6.
• Add: 3/6 + 2/6 = 5/6.

Mixed numbers (like 2 1/4): either add the whole numbers and fractions separately, or convert to improper fractions first, then add.

Tip: Always simplify your final answer. For example, 2/4 simplifies to 1/2. If the numerator ends up bigger than the denominator (an improper fraction like 7/6), you can rewrite it as a mixed number (1 1/6).