How to Add & Subtract Fractions

Most elementary and middle school students find fractions fairly easy when they first encounter them. However, when you throw addition and subtraction into the mix, subtractions become quite difficult. Adding and subtracting fractions is often confusing because of the denominator. Just what are you supposed to do with it, anyway? By taking the process apart and analyzing each step, many students find adding and subtracting with fractions to be a little bit easier. Here are some tips you can use to make adding and subtracting fractions a little bit easier.

Instructions

Difficulty: Moderately Easy

Things You’ll Need:

• Paper
• Pencil

1. Look at the fractions and see if they have the same denominator. If they do, it is called having a common denominator. Add the fractions by adding or subtracting the numerators and keeping the denominators the same (1/3 + 1/3 = 2/3).
2. Change any fractions that do not have a common denominator. You cannot add them until the denominators are the same.
3. Find the least common multiple of the fractions. This requires that you factor them down into their prime factorization. For example, if the problem is 7/10 - 7/15, you will factor 10 into 5 * 2 and 15 into 5 * 3.
4. Look at each prime factorization and choose whichever number has the most of a particular factor. In the example, the 10 has the most 2s and the 15 has the most 3s. Write these down, and then write down any factors that they share, but just write these shared factors one time. This gives you 2, 3, and 5 in this example, which you will multiply together to get 30, which will be your common denominator.
5. Change the fractions into an equal fraction by multiplying the numerator and the denominator by the same number. In the example, you will multiply 7/10 by 3/3 to give you 21/30, and you will multiply the 7/15 by 2/2 to give you 14/30.
6. Add or subtract as required since you now have a common denominator. In this example, you will get 7/30.
7. Reduce your answer if needed. You cannot reduce 7/30.

Tips & Warnings

• When you multiply by a fraction that has the same number in the numerator as the denominator, you will be multiplying by a fraction that is equal to 1, and since you are multiplying by an equivalent of 1, you are not changing the value of the fraction.
• Always reduce or simplify your answer. Sometimes when adding you will get an improper fraction, which you need to change into a mixed number.