Adding Fractions (with Different Denominators)

How to add fractions with different denominators

You can only add fractions when their denominators (bottom numbers) are the same. So the trick is to first rewrite both fractions over a common denominator, then add the numerators (top numbers). Use the animation above to watch each step for 20 problems, then follow the written method.

The method — step by step

1. Find the common denominator — the LCM (lowest common multiple) of the two denominators.
2. Make equal fractions: multiply the top and bottom of each fraction by the same number so its denominator becomes the common denominator.
3. Add the numerators and keep the common denominator.
4. Simplify the answer by dividing the top and bottom by their HCF, if possible.

Worked example: 1/4 + 1/6

1. Common denominator = LCM(4, 6) = 12.
2. 1/4 = 3/12 (multiply top and bottom by 3);   1/6 = 2/12 (multiply by 2).
3. Add: 3/12 + 2/12 = 5/12.
4. 5 and 12 share no common factor, so 5/12 is already in simplest form.

So 1/4 + 1/6 = 5/12.

Another example: 2/3 + 1/6

LCM(3, 6) = 6. Then 2/3 = 4/6, and 1/6 stays. 4/6 + 1/6 = 5/6. Answer: 5/6.

Common mistakes to avoid

• Adding the denominators — never do 1/4 + 1/6 = 2/10. Only the numerators are added, once the denominators match.
• Changing only the bottom — when you multiply the denominator, you must multiply the numerator by the same number.
• Forgetting to simplify the final answer.

Practice problems

Try these in the animation above: 3/4 + 1/6, 2/5 + 3/10, 1/4 + 3/8, 5/6 + 1/4, 1/3 + 3/5.

Quick tip

Multiplying a fraction's top and bottom by the same number does not change its value — 1/4 and 3/12 are the same amount of pizza, just cut into more slices. That's why finding a common denominator is allowed.