How to subtract fractions

Subtracting fractions works just like adding them, only taking away. The bottom number says what size the pieces are, the top number says how many you have, and you can only take pieces away from pieces of the same size.

The rule

When the bottom numbers are the same, take the second top number away from the first and keep the bottom number. When they are different, change the fractions into equal fractions with the same bottom number first.

How to do it

Look at the bottom numbers. If they are the same, go straight to taking away.
If they are different, find a number that both bottom numbers divide into, best of all their lowest common multiple.
Change each fraction to have that bottom number, multiplying its top and bottom by the same number.
Take the second top number away from the first, and write the answer over the bottom number. The bottom number stays as it is.
Simplify if you can, by dividing the top and the bottom by the same number.

Worked examples

What is 5/6 − 2/6?

5/6 − 2/6 = 3/6 = 1/2

The bottoms match, so take 2 of the 5 sixths away, and 3 sixths are left. 3 and 6 both divide by 3, so 3/6 is the same as 1/2.

What is 3/4 − 1/2?

1/2 = 2/4
3/4 − 2/4 = 1/4

4 is in the 2 times table, so quarters will do. A half is 2 quarters, and 3 quarters take away 2 quarters leaves 1 quarter.

What is 5/6 − 1/4?

The LCM of 6 and 4 is 12
5/6 = 10/12 and 1/4 = 3/12
10/12 − 3/12 = 7/12

Sixths and quarters both fit into twelfths. Multiply 5/6 top and bottom by 2, and 1/4 top and bottom by 3. 7 and 12 share no factor but 1, so 7/12 cannot be simplified.

What is 1 − 3/8?

1 = 8/8
8/8 − 3/8 = 5/8

A whole number has no bottom number to match, so write it as a fraction first. One whole is 8 eighths, and 8 eighths take away 3 eighths leaves 5 eighths.

Taking away from a mixed number

Take the whole numbers away, then the fractions: 3 3/4 − 1 1/4 = 2 2/4, which simplifies to 2 1/2.

If the fraction in the first number is too small, exchange one whole for pieces, the way long subtraction exchanges a ten for ones. In 2 1/4 − 3/4 you cannot take 3 quarters from 1 quarter, so change one of the wholes into 4/4. 2 1/4 becomes 1 5/4, and 1 5/4 − 3/4 = 1 2/4, which is 1 1/2.

Another way is to turn the mixed number into an improper fraction first: 2 1/4 = 9/4, and 9/4 − 3/4 = 6/4, which is 1 2/4 or 1 1/2 again.

Why the bottom number stays the same

The bottom number names the pieces. 5 sixths take away 2 sixths leaves 3 sixths, the same way 5 apples take away 2 apples leaves 3 apples. Nothing happened to the size of the pieces, so the bottom number does not change.

If the bottoms were taken away too, 5/6 − 2/6 would give 3/0, which means nothing at all. That is a good reminder that only the tops are counted.

To check an answer, add it back to the fraction you took away. You should get the one you started with: 7/12 + 3/12 = 10/12, which is 5/6.

Where mistakes happen

Taking away the bottoms as well as the tops. 3/4 − 1/2 done that way gives 2/2, which is 1, more than the 3/4 you started with. Taking something away can never leave more than you had.
Taking the tops away before the bottoms match. 5/6 − 1/4 is not 4/6, because sixths and quarters are different sizes. Change both into twelfths first: 10/12 − 3/12 = 7/12.
Changing the bottom number but not the top. A half in quarters is 2/4, not 1/4.
With mixed numbers, taking the smaller fraction from the bigger one, whichever comes first. In 2 1/4 − 3/4, doing 3/4 − 1/4 gives 2 2/4, but the right answer is 1 1/2. Exchange a whole instead.

Questions people ask

Do I have to simplify the answer?

3/6 and 1/2 are the same amount, so 3/6 is not wrong, just not finished, and most school tests want the simplest form. In the Math Basics practice the answer is left as it comes out, 3/6 rather than 1/2, so that the taking away is what gets practised.

What if the second fraction is bigger than the first?

Then the answer is less than zero. 1/4 − 3/4 = −2/4, which is −1/2. At primary school the bigger fraction comes first, and the Math Basics practice always puts it first.

How do I know which fraction is bigger?

Give them the same bottom number and compare the tops, or see comparing fractions for other ways.

How do I check my answer?

Add it back. Your answer plus the fraction you took away should give the fraction you started with. For 3/4 − 1/2 = 1/4, check that 1/4 + 2/4 = 3/4.