You may want to review reducing fractions first.

Adding and subtracting fractions is easiest when both fractions have the same denominator. In that case, you just need to add or subtract the numerators. If the fractions have signs, those go with the numerators. You can keep the same denominator that you already have. For example, to add −2 ⁄ 5 + 1 ⁄ 5, you just add −2 and 1, getting −1. You keep the denominator you already have, 5, so your answer is −1 ⁄ 5.

If your fractions don't have the same denominator, you're not ready to add or subtract them yet. First, you have to give them the same denominator, by “un-reducing” them. That is, you multiply the numerator and denominator by the same number. For example, if you have to subtract 9 ⁄ 4 − 1 ⁄ 3, you can un-reduce 9 ⁄ 4 by multiplying the numerator and denominator both by 3. This gives you 27 ⁄ 12. Similarly, you can un-reduce 1 ⁄ 3 by multiplying the numerator and denominator both by 4, which gives you 4 ⁄ 12. Now, 27 ⁄ 12 and 4 ⁄ 12 have the same denominator, so you can subtract them, so your answer is 23 ⁄ 12.

- In the example above, we needed to un-reduce both fractions. Sometimes, we can get away with only un-reducing one of them. So long as they have the same denominator, you can go ahead and add or subtract them.
- Some students get confused about when they can multiply by different numbers and when they have to multiply by the same number. When un-reducing a fraction, it's just like reducing; you have to multiply the numerator and denominator by the same number. But, if you're un-reducing both fractions, you can use one number for one fraction and a different number for the other fraction.
- As always, a whole number is the same thing as a fraction with denominator 1. So, if you have to subtract 2 ⁄ 3 − (−2), −2 is the same thing as −2 ⁄ 1. We can un-reduce that to −6 ⁄ 3 (multiplying the numerator and denominator both by 3). Now both fractions have the same denominator 3, so you can subtract them and get 8 ⁄ 3.
- As always, remember to reduce your answer at the end, if you can.