How to Add Two Simple Fractions With Different Denominators

Adding fractions requires the denominators (the bottom numbers) to be the same. This article tells students (or anyone else interested) how to add two fractions that have different denominators.

Things You'll Need

• paper
• pencil or pen

Instructions

1. In order to add fractions, the denominators must be the same. They are called common denominators. If you have a problem such as 2/5 + 1/5, you already have a common denominator, so just add the numerators (the top numbers) to get 2+1 or 3. The answer would be 3/5.

2. If you have to add two fractions with unlike denominators (such as 1/4 + 1/5), you must first find a common denominator (also called a least common multiple). In this example, what number is a multiple of BOTH 4 and 5?

3. List the multiples of each denominator. Multiples of 4 are 4, 8, 12, 16, 20, 24, and so on. Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, and so on.

4. Look at the two lists of multiples. Do you see a number that is in both lists. Is it the lowest number in both lists? Finding the lowest number in both lists will help you when simplifying your final answer. 20 is in both lists, and is a common denominator.

5. The original problem was 1/4 + 1/5. We just said 20 was a common denominator, so the next step is to rewrite each fraction so that 20 is the denominator. 1/4 is the same as 5/20. We multiplied the denominator (4) by 5, so we must multiply the numerator (1) by the same amount in order to keep the value of the fraction the same. 1/5 is the same as 4/20. We multiplied the denominator (5) by 4, so we must multiply the numerator (1) by the same amount in order to keep the value of the fraction the same.

6. Now we have 5/20 + 4/20. We have a common denominator (20), so just add the numerators. 5+4=9, so the final answer is 9/20.

Tips & Warnings

• It helps to know multiples of numbers. For example, some multiples of 3 are 3, 6, 9, and 12, and some multiples of 7 are 7, 14, 21, and 28.

• Be sure to simplify your answers!

• If you have two fractions with the same numerator but different denominators, DO NOT simply add the numerators and then add the sum of the denominators.

• If you haven't mastered adding two whole numbers yet, then adding fractions is difficult.