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How to Add and Subtract Fractions

Level 2 Fractions · Reviewed by The NumThink editorial team · Last reviewed

Short version: Same denominator: add the tops, keep the bottom (2/7 + 3/7 = 5/7). Different denominators: first rewrite both over a common denominator (1/2 + 1/4 = 2/4 + 1/4 = 3/4).

This page is part of the NumThink Fractions course. Read why the method works, watch it run on worked examples, then drill it in the practice box below until it feels automatic.

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Why it works

Sevenths plus sevenths are sevenths, just as apples plus apples are apples: 2 sevenths and 3 sevenths make 5 sevenths. The denominator is the unit — it is never added.

Halves and quarters are different units, so first change them into the same unit with an equivalent fraction: 1/2 = 2/4. Then 2/4 + 1/4 = 3/4.

The steps

  1. Check the denominators. The same? Go straight to the last step. Different? Find a common denominator — a number both divide into.
  2. Rewrite each fraction. 1/3 + 1/4: the common denominator is 12, so 1/3 = 4/12 and 1/4 = 3/12.
  3. Add or subtract the numerators, keep the denominator. 4/12 + 3/12 = 7/12.

Worked examples

Easy 2/7 + 3/7

Show the thinking

Same denominator: 7

2 + 3 = 5

So 2/7 + 3/7 = 5/7.

Answer: 5/7

Medium 1/2 + 1/4

Show the thinking

1/2 = 2/4

2/4 + 1/4 = 3/4

So 1/2 + 1/4 = 3/4.

Answer: 3/4

Hard 2/3 + 1/4

Show the thinking

Common denominator: 12

2/3 = 8/12 and 1/4 = 3/12

8/12 + 3/12 = 11/12

So 2/3 + 1/4 = 11/12.

Answer: 11/12

When to use it

  • Recipes and measurements: 1/2 cup + 1/3 cup = 5/6 cup.
  • Whenever the answer must be exact — decimals lose precision (1/3 is 0.333…).

When NOT to use it

  • Tenths and quarters can be quicker as decimals: 3/10 + 1/4 = 0.3 + 0.25 = 0.55.
  • Multiplying fractions follows a different rule — multiply the tops and the bottoms: 2/3 × 3/4 = 6/12 = 1/2.

Common mistakes

Adding the denominators. Writing 1/2 + 1/4 as 2/6. Fix: The denominator is the unit — it stays. Rewrite in quarters first: 2/4 + 1/4 = 3/4.
Rewriting only the denominator. Changing 1/2 + 1/4 into 1/4 + 1/4. Fix: When the bottom is doubled (2 → 4), the top must be doubled too: 1/2 = 2/4.
Check yourself: Estimate first: 2/3 + 1/4 should be a little under 1 (2/3 plus 1/3 would make exactly 1), and 11/12 is just under 1 ✓.