Subtraction of Fractions

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Fractions Units

Subtracting fractions is done differently than the usual numbers. Normally, while adding or subtracting fractions you will find two types of problems:

Type 1: where the fractions being added or subtracted have the same denominator eg.

Type 2: where the fractions being added or subtracted have different denominators eg.

As you know, fractions represent parts of the whole. So, when these parts are from the whole broken into same number of parts it is easy to subtract them.
For Type 1 problems, we just need to subtract the top parts (numerator) of the fractions and leave the denominator as such. So, to solve the problem in the above example the solution will be:

For Type 2 problems where the denominator is different, we can not subtract these fractions by simply subtracting the numerators. In order to solve these problems first we will need to make into fractions with the same denominator. See how this is done in examples below.

Examples

Example 1

changing both fractions to a common denominator (see comments on the right)

Comments:

To solve this problem, first we will need to look at the denominators 5 and 2 and see what multiples of these numbers are common.

Multiples of 5 are:
5 10 15 20 25

Multiples of 2 are:
2 4 6 8 10 12 14

so, in multiples of 5 and 2 the least common multiple is 10.
now, we will change 4/5 and 1/2 into their equivalent fractions with denominator 10:

Example 2

Changing them to simple fractions we find:

Now, changing both fractions to a common denominator (see comments on the right)we can solve it as:

This fraction can be further simplified as:

Comments:
It is always good to convert these mixed fractions into simple fractions before working out subtraction. We can do this using the technique shown on the right. Multiply the denominator with the whole number and add the product to the numerator. Re-write the fraction with this sum as numerator.

Next, we need to look at the denominators and see what multiples of them are common:

Multiples of 3:
3 6 9 12 15 18 21

Multiples of 5:
5 10 15 20

So, we find that 15 is the least common multiple.

Have a Go

Problem 1

Problem 2

Practice Questions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Solution 1

First we will simply to make simple fractions

Now, we need to find the least common multiple of 3 and 4:
3= 3 6 9 12 15
4= 4 8 12 16
Now we need to convert both fractions to a common denomintor of 12

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Solution 2

Here is a mixed problem. First we will change everything to a simple fraction then solve the sum one step at a time.

Now, find the least common multiple for 6, 3 and 4
6= 6, 12, 18
3= 3, 6, 9, 12, 15, 18
4= 4, 8, 12, 16
So, converting the fractions to a common denominator of 12 we get:

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