How to Subtract Fractions

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: \displaystyle \frac{8}{15} - \frac{3}{15}.

Solution

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, 

\displaystyle \frac{8}{15} - \frac{3}{15} = \frac{5}{15}.

We reduce to lowest term by dividing both the numerator and denominator of \frac{5}{15} by 5. This results to \frac{1}{3} which is the final answer.

Example 2: \displaystyle \displaystyle \frac{3}{5} - \frac{1}{2}.

Solution

The two fractions are dissimilar, so we must find their least common denominator. To do this, we  find the least common multiple of 2 and 5. The  common multiples of 2 are

2, 4, 6, 8, 10, 12 and so on

and the common multiples of 5 are

5, 10, 15, 20, 25 and so on.

As we can see from the lists above, 10 is the least common multiple of 2 and 5.

We now change the denominator of both fractions to 10.

First, we find the equivalent fraction of \frac{3}{5}. That is,

\displaystyle \frac{3}{5} = \frac{x}{10}.

To find the value of x,  divide 10 by 5 and then multiply to 3. The result is 6 which becomes the numerator of the equivalent fraction. So, the equivalent fraction of \frac{3}{5} is \frac{6}{10}.  If you are confused with this process, please read How to Add Fractions.

Now, we get the equivalent fraction of \frac{1}{2} or we find the value of y in \frac{1}{2} = \frac{y}{10}. We divide 10 by 2 and then multiply it by 1, which gives us 5. So, the equivalent fraction of \frac{1}{2} is \frac{5}{10}.

We now subtract the fractions.

\displaystyle \frac{6}{10} - \frac{5}{10} = \frac{1}{10}.

The final answer is \frac{1}{10}.

Example 3: 6 \frac{3}{4} - \frac{1}{5}

Solution

First, we convert 6 \frac{3}{4} to improper fraction. That is,

\displaystyle \frac{4 \times 6 + 3}{4} = \frac{27}{4}.

to get

\displaystyle \frac{27}{4} - \frac{1}{5}.

The least common multiple of 5 and 4 is 20 (try listing as in example 2).

Now, to get the equivalent fraction, we have \frac{27}{4} = \frac{a}{20}. Now, (20 \div 4) \times 27 = 135. This means, the equivalent fraction

\displaystyle \frac{27}{4} = \frac{135}{20}.

We also convert \frac{1}{5} to \frac{b}{20} which is equal to \frac{4}{20}.

Now, we subtract the fractions.

\displaystyle \frac{135}{20} - \frac{4}{20} = \frac{131}{20}.

 Converting the answer which is an improper fraction to mixed number, we have

\frac{131}{20} = 6 \displaystyle \frac{11}{20}.

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.

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