**How do you add fractions with different denominators?**

When adding fractions with different denominators, the first step is to make them have a common (same) denominator. Sometimes you’ll get lucky and only have to change one fraction for both of them to have the same denominator. (We’ll show you how to do that in example one below.) Other times you’ll have to change both fractions. (We’ll show you how to do that in example two.) After you modify your fractions to have the same denominator, add the numerators.

**Example 1: Add 2/3 and 1/6**

- Find the least common multiple (LCM) of 3 and 6.
- The multiples of 3 are 3, 6, 9, 12, 15, and so on.
- The multiples of 6 are 6, 12, 18, 24, 30, and so on.
- The first number that shows up in both lists is the LCM. In this case, that number is 6.

- Change the fraction(s) so they both have a denominator of 6.
- 1/6 already has a denominator of 6, so there’s nothing to do there.
- To change 2/3 ask yourself, “What do I have to multiply 3 by to make it 6?” The answer is 2.
- Now you have to take 2/3 and multiply both the numerator AND denominator by 2.
- 2×2=4, 3×2=6. So the new fraction is 4/6.

- Now that the fractions have the same denominator add them together.
- When adding fractions you add the numerators (top numbers) and keep the denominator the same.
- 4/6 + 1/6 = 5/6
- 5/6 is your answer.

**Example 2: Add 4/5 and 2/3**

- Find the least common multiple (LCM) of 5 and 3.
- The multiples of 5 are 5, 10, 15, 20, 25, and so on.
- The multiples of 3 are 3, 6, 9, 12, 15, and so on.
- The first number that shows up in both lists is the LCM. In this case, that number is 15.

- Change the fraction(s) so they both have a denominator of 15.
- Since neither fraction has a denominator of 15, you’ll have to change both fractions.
- To change 4/5 ask yourself, “What do I have to multiply 5 by to make it 15?” The answer is 3.
- Now you have to take 4/5 and multiply the numerator AND denominator by 3.
- 4×3=12, 5×3=15. So the new fraction is 12/15.
- To change 2/3 ask yourself, “What do I have to multiply 3 by to make it 15?” The answer is 5.
- Take 2/3 and multiply the numerator AND denominator by 5.
- 2×5=10, 3×5=15. So the new fraction is 10/15

- Now that the fractions have the same denominator add them together.
- When adding fractions you add the numerators (top numbers) and keep the denominator the same.
- 12/15 + 10/15 = 22/15
- 22/15 is your answer. (You can also write it as a mixed number: 1 and 7/15)

**Can you add fractions with different denominators without finding a common denominator?**

Nope. I know you wish there was a shortcut, but finding common denominators is the only way to add fractions. The good news is that the more you add fractions without common denominators the easier the process will become. At some point, you may even be able to do all the work above in your head. Wouldn’t that be cool? Keep practicing!