How to Add and Subtract Fractions: Step-by-Step Method

To add or subtract fractions, you need a common denominator. Rewrite each fraction with that shared denominator, then add or subtract just the numerators — the denominator stays the same. For example, 2/5 + 1/4 = 8/20 + 5/20 = 13/20.

Below you'll find two fully worked examples, a clean 5-step method, and the mistakes that trip most students up.

Worked example: 2/5 + 1/4

Let's walk through 2/5 + 1/4 from start to finish.

1. Find a common denominator. The denominators are 5 and 4. The least common multiple of 5 and 4 is 20.
2. Rewrite each fraction with denominator 20. Multiply 2/5 by 4/4 to get 8/20. Multiply 1/4 by 5/5 to get 5/20.
3. Add the numerators. 8 + 5 = 13.
4. Keep the denominator. The result is 13/20.
5. Simplify if possible. 13 is prime and does not divide 20, so 13/20 is already in lowest terms.

Answer: 13/20.

The 5-step method for combining fractions

1. Find a common denominator — usually the least common multiple (LCM) of the two denominators. Example: for 3 and 6, use 6.
2. Convert each fraction to an equivalent one with that denominator by multiplying top and bottom by the same number. Example: 1/2 = 3/6.
3. Add or subtract the numerators only. Example: 3/6 + 1/6 → 3 + 1 = 4.
4. Keep the common denominator — do not add denominators. Example: 3/6 + 1/6 = 4/6, not 4/12.
5. Simplify by dividing top and bottom by their greatest common factor. Example: 4/6 = 2/3.

How to find a common denominator quickly

If the denominators share no common factors (like 5 and 4), just multiply them: 5 × 4 = 20. If one denominator divides the other (like 3 and 6), use the larger one. Otherwise, list multiples of each denominator until you find the smallest match.

Worked example: 3/4 − 1/6

Subtraction uses the exact same steps as addition.

1. Common denominator. The LCM of 4 and 6 is 12.
2. Convert. 3/4 = 9/12 (multiply top and bottom by 3). 1/6 = 2/12 (multiply top and bottom by 2).
3. Subtract the numerators. 9 − 2 = 7.
4. Keep the denominator. The result is 7/12.
5. Simplify. 7 is prime and does not divide 12, so 7/12 is the final answer.

Answer: 7/12.

Common mistakes to avoid

• Adding the denominators. 1/2 + 1/3 is not 2/5. Denominators stay the same once you've converted; only numerators combine.
• Skipping the conversion step. You cannot add 2/5 + 1/4 directly as 3/9. Both fractions must first share a denominator.
• Forgetting to multiply the numerator too. When rewriting 1/4 as twentieths, multiply top and bottom by 5 → 5/20, not 1/20.
• Not simplifying at the end. 6/8 is correct arithmetic but should be reduced to 3/4.
• Sign errors with mixed numbers. Convert mixed numbers like 2 1/3 to improper fractions (7/3) first, then apply the method.

Ready to practice?

Seeing the steps once is different from being able to do them under pressure. LernOS's guided tutor walks you through problems one question at a time — nudging you toward the next step instead of just showing the answer — so the method sticks. Sign up below to try a guided fraction session and lock in what you just read.