How to Add Fractions

Every student needs to learn how to add fractions. Here's some extra help to assist your child in understanding the steps needed for adding fractions.

Numerators and Denominators
Fractions are made up of two numbers: the top number, the numerator, and the bottom number, the denominator. There are also two types of fractions. Fractions that have the same denominator are called like fractions. If the denominators are different, they're called un-like fractions. Adding like fractions is simple. You just need to add the numerators together and keep the denominator the same. For example, 3/5 + 1/5 = 4/5.

Dealing with Unlike Fractions
Things get a little bit harder when the denominators are different. You can't simply add unlike fractions; you first need to find a common denominator. Think of a pie. If you added 1/2 of a pie to 1/3 of a pie, you wouldn't have 1/5 of the pie, you'd have a lot more. There are a couple ways to get the right answer with unlike fractions.

The first way is by finding the least common denominator. You can do this by listing out the multiples of each denominator and finding the first one they have in common. For example, let's take a look at the equation 1/6 + 1/8. Notice the denominators are different. The multiples of 6 are 6, 12, 18, 24, 30, etc. The multiples of 8 are 8, 16, 24, 32, etc. Both 6 and 8 have a multiple of 24; this means that 24 is the least common denominator.

Now that we have the least common denominator, we need to convert our fractions. First let's convert 1/6. We know that 6 x 4 = 24, so we need to multiply the numerator by 4 as well. So 1/6 becomes 4/24. Now let's convert 1/8. We know that 8 x 3 = 24, so the numerator must be multiplied by 3. So now 1/8 becomes 3/24.

Once you have like fractions, you can add them. Our equation now looks like this: 4/24 + 3/24. Just add the numerators and your answer is 7/24.

Instead of finding the least common denominator and using multiples, which can take a long time to list out, here's a tip for quickly adding fractions. Let's use the example above, 1/6 + 1/8. We'll still need to find a common denominator, but we can do it easily by multiplying both fractions by the other's denominator. So we can take 1/6 and multiply its numerator and the denominator by 8 to get 8/48. Next multiply 1/8 by 6 to get 6/48. Now we can add the two fractions to get 14/48. As a final step, simplify this fraction, which equals 7/24.

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