How to Subtract Fractions
The steps to subtract fractions are very similar to those for adding or comparing fractions (not surprising, as subtracting is just adding a negative!).
Given a fraction written in the form a/b, the top part (a) is called the numerator, and the bottom part (b) is called the denominator. In order to subtract fractions, we first find a common denominator, then subtract the numerators.
Finding a Common Denominator
The denominator of a fraction represents how many pieces the item we're looking at is divided into. We want both numbers to be divided into pieces of the same size, so that we can treat each piece equally. For example, if I cut my pizza into four pizzas and you cut your pizza into eight pieces, I'm certainly not going to trade one of my slices for one of your slices!
First find the smallest common multiple of the denominators for your fractions using any convenient method, such as factor trees. As an example, suppose the two fractions are 2/3 and 1/4. The smallest common multiple of 3 and 4 is 12, so we need to rewrite both fractions in twelfths. Twelve divided by three is four, so we multiply both the top and the bottom (that is, both the numerator and the denominator) of the first fraction by four to get 8/12. Similarly, twelve divided by four is three, so we multiply both the numerator and the denominator of the second fraction by three to get 3/12.
Subtracting When You Have a Common Denominator
Now that you have a common denominator, you can subtract. Continuing the example above, we originally had a pie that was cut into three even slices and two were left, and we had a second pie cut into four even slices, where only one was left.
We then cut each of the slices in the first pie into four pieces, and we cut the slice in the second pie into 3 pieces. All of our pieces should now be the same size, so we can compare the two pies directly. We see that we have 8 pieces left in the first pie and 3 left in the second, so subtracting, we see that there are 8 – 3 = 5 more pieces left in the first pie. Each piece is 1/12 of a pie, so what's left of the first pie is 8/12, or 2/3 of a pie larger than what's left of the second pie.
Remember that any time you're adding or subtracting fractions, you first get a common denominator and then add or subtract the numerator. When you're doing your addition or subtraction, the denominator does not change.
Now that you know the steps to subtract fractions, see if you can solve these math problems. The answers are given below.
1) What is 6/7 – 1/2?
2) What is 2/3 less than 4/5?
3) What is the difference of 2/3 and 1/2?
Answers to the Sample Problems
1) The lowest common multiple of 7 and 2 is 14, so we multiply 6/7 by 2/2 and 1/2 by 7/7, which gives us the new problem 12/14 – 7/14. Subtracting, we get 5/12.
2) The lowest common multiple of 3 and 5 is fifteen, so we'll rewrite the problem as 12/15 – 10/15. (Notice that we're asked for 2/3 less than 4/5, which is the same as 4/5 – 2/3). 12-10=2, so the answer is 2/15.
3) Difference means the result of a subtraction problem; the question is asking what is 2/3 – 1/2. After getting a common denominator, we have 4/6 – 3/6, which gives us a result of 1/6.
This post is part of the series: Explore and Understand Fractions
- How to Divide Fractions: Step by Step
- How to Find the Least Common Denominator
- Steps to Subtracting Fractions