Fractions

The procedures for addition and subtraction of fractions are similar. For more explanation see Addition of Fractions.

Subtracting like fractions

Example 1: 7/8 - 2/8 = 5/8 (7 eighths - 2 eighths = 5 eighths)

Let's say I have 7/8 of a metre of wood and I give you 2/8 of a metre. How much wood do I have left?

Setting Out

Thinking

I start with 7/8 of a metre of wood,

I give you 2/8.

That leaves 5/8 of a metre of wood.

Subtracting unlike fractions

Example 2: 1/3 - 2/9 = 1/9

To subtract unlike fractions we first need to find a common denominator. If you would like further explanation see the 'finding common denominators' section in Key Ideas.

Setting Out

Thinking

If I want to subtract 2/9 from 1/3 I need to find a number which is a multiple of both 3 and 9 and make this the common denominator.

3 x 3 = 9

1 x 9 = 9

3 and 9 are factors of 9, so 9 will be a common denominator.

I need to turn thirds into ninths.

I know 1 third is equivalent to 3 ninths so I can rename 1 third as 3 ninths.

(I could have changed 1 third into 3 ninths by multiplying 1/3 by 3/3)

Now I can subtract 2 ninths from 3 ninths to give an answer of 1 ninth.

Example 3: 5/6 - 1/12 = 3/4

Click the image to see the movie

Subtracting mixed numbers - regrouping:

Example 4: 24 2/5 - 16 4/5 = 7 3/5

We have used the vertical method to solve this problem. Using this method we can clearly show how we have regrouped or renamed the fractions so that we can perform the subtraction.

Question

Setting Out

Thinking

We cannot subtract from but we can convert 1 into . So,

By regrouping 24 and 2 fifths into 23 and seven fifths we have turned a difficult subtraction problem into an easy subtraction problem.

Example 5: using the vertical method, 4 2/7 - 1 3/7 = 2 6/7

Click the image to see the movie

General rule for subtraction of fractions

There is also a general rule which can be used to solve subtraction of fractions problems. This rule is similar to that which was shown for addition of fractions. It is not always the most efficient method to use. If you are not sure why, see Addition of fractions.

Steps for subtraction of fractions

To subtract fractions:

Step 1: Check to see if the fractions have the same denominator. If they haven't, then find a common denominator.

Step 2: Make 'like' fractions

Step 3: Subtract the 'like' fractions

Step 4: Simplify the answer if required.

Quick quiz

Perform the following subtractions. Express your answers using the lowest possible denominator.

1.
2.
3.
4.
5.
6.

To view the quiz answers, click here.