We have already learned the three operations on fractions namely addition, multiplication, and division. In this post, we are going to learn the last elementary operation: subtraction. If you have mastered addition of fractions, this will not be a problem for you because the process is just the same. Let’s subtract fractions!
Example 1: .
The given is a similar fraction (fraction whose denominators are the same), so just like in addition, we just perform the operation on the numerators. Therefore, we just have to subtract the numerator and copy the denominator. That is,
We reduce to lowest term by dividing both the numerator and denominator of by . This results to which is the final answer.
Example 2: .
The two fractions are dissimilar, so we must find their least common denominator. To do this, we find the least common multiple of and . The common multiples of 2 are
and so on
and the common multiples of are
and so on.
As we can see from the lists above, is the least common multiple of and .
We now change the denominator of both fractions to .
First, we find the equivalent fraction of . That is,
To find the value of , divide by and then multiply to . The result is which becomes the numerator of the equivalent fraction. So, the equivalent fraction of is . If you are confused with this process, please read How to Add Fractions.
Now, we get the equivalent fraction of or we find the value of in . We divide by and then multiply it by , which gives us . So, the equivalent fraction of is .
We now subtract the fractions.
The final answer is .
First, we convert to improper fraction. That is,
The least common multiple of and is (try listing as in example 2).
Now, to get the equivalent fraction, we have . Now, . This means, the equivalent fraction
We also convert to which is equal to .
Now, we subtract the fractions.
Converting the answer which is an improper fraction to mixed number, we have
There is another way to make the solution of the third examples shorter. We will discuss this in the next post which is subtraction of fraction involving mixed fractions.