# Steps to Subtract Fractions

Welcome to the Math Salamanders Steps to Subtract Fractions support page.

Here you will find some helpful support in learning how to subtract fractions.

## Steps to Subtract Fractions

### How do you Subtract Fractions Support

For those of you who like to see some algebra, here is the simple formula for subtracting two fractions:

Formula for subtracting two fractions

${a \over b} - {c \over d} = {ad - bc \over bd}$

Frazer says "Here are 3 simple steps to subtract two fractions." Before you start...

Convert any mixed fractions into improper fractions.

Step 1

Convert the fractions to the same denominator.

If the fractions already have the same denominator, you do not need to do anything!

Step 2

Subtract the second numerator from the first numerator, keeping the denominator the same, to get the answer.

Step 3 (optional)

You may want to convert this into simplest form by cancelling common factors.

See below for a step-by-step breakdown of how to add fractions.

Step 1: Convert the fractions to the same denominator.

If the fractions already have the same denominator, skip the rest of this part.

If the fractions have different denominators, keep reading!

We can only subtract two fractions together if they have the same denominator.

It is a bit like when you are subtracting two amounts, one given in inches and one in centimetres - you need to convert both measures to the same units - either centimetres or inches - before you do the subtraction!

There are two different possibilities for the this step:

Step 1a) If one of the denominators is a multiple of the other denominator.

If this is the case, you just need to multiply the numerator and denominator of the fraction with the lower denominator so that the two denominators are the same.

Step 1b) If one of the denominators is not a multiple of the other denominator.

The easiest and simplest way to convert the two fractions to equivalent fractions with the same denominators is to multiply the numerator and denominator of each fraction by the other fraction's denominator.

Step 2: Subtract the second numerator from the first

Once the two fractions have the same denominator, we can subtract the second numerator from the first one.

This will give us the answer we are looking for.

Have a look at the examples below to see how it all works!

### Steps to Subtract Fractions - Examples

#### Example 1) Work out ${4 \over 5} - {7 \over 15}$

Step 1)

You will notice that the second denominator (15) is a multiple of the first denominator (5) so we need to follow Step 1a)

So we need to multiply the numerator and denominator of the first fraction by 3.

This gives us: ${4 \over 5} = {4 \times 3 \over 5 \times 3} = {12 \over 15}$

So we now have: ${4 \over 5} - {7 \over 15} = {12 \over 15} - {7 \over 15}$

Step 2)

Now the denominators are equal, all we need to do now is to subtract the second numerator from the first.

So we have: ${12 \over 15} - {7 \over 15} = {12 - 7 \over 15} = {5 \over 15}$

Step 3)

We need to write this answer in simplest form, so divide the numerator and denominator by a common factor of 5!

${5 \over 15} = {5 ÷ 5 \over 15 ÷ 5} = {1 \over 3}$

Final answer: ${4 \over 5} - {7 \over 15} \; = \; {1 \over 3}$

#### Example 2) Work out ${6 \over 7} - {2 \over 5}$

Step 1)

The denominator of the first fraction is 7. The denominator of the second fraction is 5. These numbers are not multiples of one another.

We need to use Step 1b)

So we multiply the numerator and denominator of the first fraction by the second fraction's denominator (5).

This gives us: ${6 \over 7} = {6 \times 5 \over 7 \times 5} = {30 \over 35}$

Next we multiply the second fraction's numerator and denominator by the first fraction's denominator (7).

This gives us: ${2 \over 5} = {2 \times 7 \over 5 \times 7} = {14 \over 35}$

We have now converted the two fractions into fractions with like denominators, and changed our subtraction to: ${6 \over 7} - {2 \over 5} = {30 \over 35} - {14 \over 35}$

Step 2)

Now the denominators are equal, all we need to do now is to subtract the second numerator from the first.

${30 \over 35} - {14 \over 35} = {30 -14 \over 35} = {16 \over 35}$

Step 3)

This fraction is already in simplest form, so we don't need to do anything else!

Final answer: ${6 \over 7} - {2 \over 5} \; = \; {16 \over 35}$

#### Example 3) Work out ${9 \over 4} - {5 \over 6}$

Step 1)

The denominator of the first fraction is 4. The denominator of the second fraction is 6. These numbers are not multiples of one another.

We need to use Step 1b)

So we multiply the numerator and denominator of the 1st fraction by 6 and the numerator and denominator of the 2nd fraction by 4.

This gives us: ${9 \over 4} - {5 \over 6} = {9 \times 6 \over 4 \times 6} - {5 \times 4 \over 6 \times 4} = {54 \over 24} - {20 \over 24}$

Step 2)

Now the denominators are equal, all we need to do now is to subtract the second numerator from the first.

${54 \over 24} - {20 \over 24} = {54 - 20 \over 24} = {34 \over 24}$

Step 3)

We need to simplify this fraction by dividing the numerator and denominator by common denominator 2.

${34 \over 24} = {34 ÷ 2 \over 24 ÷ 2} = {17 \over 12}$

Converting this to a mixed number gives us: ${17 \over 12} = 1 {5 \over 12}$

Final answer: ${9 \over 4} - {5 \over 6} \; = \; {17 \over 12} \; or \; 1 {5 \over 12}$

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