How to Subtract Fractions With Different Denominators

Published 3 August 2021 · Updated 5 August 2026

To subtract fractions with different denominators, rewrite both fractions over a common denominator, subtract the numerators, and leave the denominator as it is. So 4/5 - 1/3 becomes 12/15 - 5/15, which gives 7/15. The only real work is finding a denominator both fractions can share and building the equivalent fractions that go with it.

The denominator is the bottom figure, and it shows how many equal parts one whole has been split into. The numerator is the top figure, and it shows how many of those parts you have. You can only take one fraction away from another when both wholes have been cut the same way, which is why the denominators have to match before anything else happens.

The same rules apply to proper fractions, where the numerator is smaller than the denominator, and to improper fractions, where the numerator is greater than the denominator. Mixed numbers follow the same route once you convert them into improper fractions first.

The method below is the one to use when you have to show your working in an exam. Subtracting fractions that already share a denominator is a shorter job, since you can skip straight to the subtraction.

How to subtract fractions with different denominators in four steps

Step 1: Find the least common denominator

The least common denominator (LCD) is the lowest common multiple of the two denominators you’re working with.

Say we’re asked to subtract 2/6 from 2/3, which we write as 2/3 - 2/6. Here 6 is a multiple of 3, so 6 is our LCD.

When neither denominator divides into the other, list the multiples of the larger one until you reach a number the smaller one divides into. If the two share no factors at all, multiplying them together always gives a workable common denominator.

Step 2: Find the equivalent fractions

Changing a denominator must not change the value of the fraction, so whatever you multiply the bottom by, you multiply the top by as well.

To turn the denominator 3 into 6 we multiply by 2, so the numerator 2 is multiplied by 2 as well. That gives 4/6, the equivalent fraction for 2/3.

Repeat the process for the second fraction. In this example 2/6 already has the denominator we want, so it stays as it is.

We now have a revised equation of 4/6 - 2/6.

Step 3: Subtract the new numerators

Subtract the second numerator from the first and write the result over the common denominator. In this case, 4 - 2 = 2, which gives 2/6.

The denominator itself never changes at this stage. Subtracting the denominators as well as the numerators is the most common mistake in this topic, and it produces an answer that is nowhere near the right size.

Step 4: Simplify the answer if necessary

The last step is to simplify the fraction if possible. To do this, you’ll need to find the highest common factor shared by both parts of the fraction and divide them by it.

In the case of 2/6, the highest common factor is 2. Since 2 ÷ 2 = 1, and 6 ÷ 2 = 3, our simplified fraction is 1/3.

2/3 - 2/6 = 1/3

If the result is an improper fraction, convert it into a mixed number when the question asks for one.

Equivalent fractions, the skill underneath the method

Two fractions are equivalent when they describe the same amount written with different numbers. Multiply the numerator and the denominator by the same whole number and the result is always an equivalent fraction.

Starting from 2/3: 2/3 = 4/6 = 6/9 = 8/12 = 10/15 = 20/30. Every one of those is worth the same, and 2/3 is the simplest form because 2 and 3 share no common factor.

So 4/6 is equivalent to 2/3. Both parts of 2/3 have been multiplied by 2 to get there, and dividing 4/6 by 2 top and bottom takes you straight back.

To test whether two fractions are equivalent without simplifying either of them, cross multiply. For 4/6 and 2/3, 4 × 3 = 12 and 2 × 6 = 12, and equal products mean equivalent fractions. For 4/6 and 3/5, 4 × 5 = 20 while 3 × 6 = 18, so those two are not equivalent.

This is the same skill the subtraction method relies on. Finding a common denominator is nothing more than rewriting both fractions as equivalent fractions that happen to share a bottom number.

Example questions

Below you’ll find four worked examples. The first two are standard equations, the third is a word problem, and the fourth involves mixed numbers.

Example question 1

What is 4/5 minus 1/3?

5 and 3 share no factors, so multiplying them gives our common denominator: 5 × 3 = 15.

For the first fraction, 5 × 3 = 15, so the numerator is also multiplied by 3: 4 × 3 = 12. Our first equivalent fraction is 12/15.

For the second, 3 × 5 = 15, so 1 × 5 = 5. Our second equivalent fraction is 5/15.

Subtract the numerators and place the result over the common denominator: 12/15 - 5/15 = 7/15.

15 is not a multiple of 7, so 7/15 is already in its simplest form.

Answer: 4/5 minus 1/3 = 7/15

Example question 2

What is 5/6 minus 13/25?

Start by finding the LCD. In this example it’s not quite as straightforward, so you might find it useful to write down multiples of the highest current denominator to help you: 25, 50, 75, 100, 125, 150…

Now we can see the first multiple of 25 divisible by 6 is 150, so this is our LCD.

Next, we need to find our equivalent fractions:

6 x 25 = 150, so we need to use the same value to multiply the numerator, giving 5 x 25 = 125. Our first equivalent fraction is therefore 125/150.

Now move on to the second:

25 x 6 = 150 and 13 x 6 = 78. Our second equivalent fraction is 78/150.

Subtract the numerators and place the result over the LCD: 125/150 - 78/150 = 47/150.

This fraction is already in its simplest form.

Answer: 5/6 minus 13/25 = 47/150

Example question 3

Emma is training for a marathon and has set herself a target distance to reach by the end of the week. On Monday, she runs 7/15ths of the distance. On Wednesday, she runs 4/5ths of the distance.

How much further did Emma run on Wednesday compared to Monday?

To solve this problem, we need to subtract how far Emma ran on Monday from how far she ran on Wednesday, so would write our equation as: 4/5 - 7/15.

Next, we find our LCD, which we can see is 15. We find the equivalent of our first fraction by multiplying both parts by the same value: 5 x 3 = 15 and 4 x 3 = 12.

Our equivalent fraction is therefore 12/15.

As our denominator is already 15 in the second fraction, no change is required here.

We can now subtract our numerators (12 - 7 = 5) and place our answer over the denominator: 5/15.

Finally, we identify the highest common factor of 5 and 15 as 5, and divide both parts of the fraction to simplify: 5 ÷ 5 = 1 and 15 ÷ 5 = 3.

Answer: 4/5 minus 7/15 = 1/3

Example question 4

What is 3 1/4 minus 1 5/6?

Convert both mixed numbers into improper fractions first. For 3 1/4, multiply the whole number by the denominator and add the numerator: 3 × 4 = 12, and 12 + 1 = 13, giving 13/4. For 1 5/6, 1 × 6 = 6, and 6 + 5 = 11, giving 11/6.

Now find the common denominator. 4 and 6 both divide into 12, so the LCD is 12.

13/4 becomes 39/12, because 4 × 3 = 12 and 13 × 3 = 39. 11/6 becomes 22/12, because 6 × 2 = 12 and 11 × 2 = 22.

Subtract the numerators: 39/12 - 22/12 = 17/12.

17 and 12 share no common factor, so the fraction will not simplify, but it is improper and the question uses mixed numbers. 12 goes into 17 once with 5 left over, so 17/12 = 1 5/12.

Answer: 3 1/4 minus 1 5/6 = 1 5/12

A quicker method when the denominators share no factors

When neither denominator divides into the other and the two share no factors, you can subtract in one line. Multiply the numerator of each fraction by the other denominator, subtract, and put the result over the product of the two denominators.

For 3/4 - 2/7: 3 × 7 = 21 and 2 × 4 = 8, so the numerator is 21 - 8 = 13. The denominator is 4 × 7 = 28, giving 13/28.

This is faster, but it does not always land on the lowest common denominator, so check whether the answer simplifies. For 5/6 - 1/4 the same method gives (5 × 4 - 1 × 6) over 24, which is 14/24, and that simplifies to 7/12.

Mistakes that cost marks

• Subtracting the denominators as well as the numerators. The denominator stays put once both fractions share it.
• Changing the denominator without changing the numerator, which quietly alters the value of the fraction.
• Subtracting the fractions the wrong way round. Unlike addition, order matters, so read the question carefully when it says one amount is taken from another.
• Stopping before you simplify. An answer that is correct but unsimplified often loses the mark.
• Leaving mixed numbers in place. Convert them to improper fractions before you look for a common denominator.

Practice subtracting fractions

Fraction subtraction rarely appears as a bare sum in an aptitude test. It sits inside percentage change, share of budget and remaining stock questions, where the arithmetic has to be quick and reliable rather than elegant.

Try numerical reasoning tests for the data driven versions, basic numeracy tests to drill the arithmetic itself, and the free aptitude tests if you want to see where your speed stands before you commit to a full practice set.