Why can't I just add the tops and the bottoms?

Because the denominator tells you the size of each piece, not how many pieces you have. 1/3 + 1/4 is not 2/7, since 2/7 is smaller than 1/3 on its own. You can only add pieces once they are the same size, which is why you need a common denominator.

Do I have to use the lowest common denominator?

No. Any common denominator gives the right answer. Multiplying the two denominators together always works. The lowest one just keeps the numbers smaller, so there is less to simplify at the end.

Should I leave my answer as an improper fraction or a mixed number?

Both are correct. If the question uses mixed numbers, give a mixed number. In algebra and later maths, improper fractions are often more useful. Always simplify either way.

Maths explained

Adding and subtracting fractions, explained step by step

How to add and subtract fractions with the same or different denominators, and with mixed numbers, using worked examples, common mistakes and practice.

For students. By the Qlive team. 7 September 2026 . 4 min read.

This guide is for you if fractions still make you nervous. In CBSE, adding and subtracting fractions is taught across Classes 4 to 7, and the same skill runs through Key Stage 2 and 3 in the UK. It is not a topic you leave behind: GCSE, IGCSE and CBSE Class 10 questions on algebra, probability and ratio all assume you can do it quickly and accurately. A few clear rules are all you need.

The idea in plain words

A fraction has two parts:

The denominator (bottom) tells you how many equal pieces the whole is cut into. It is the size of each piece.
The numerator (top) tells you how many of those pieces you have.

You can only add or subtract pieces that are the same size. So:

If the denominators are the same, add or subtract the numerators and keep the denominator.
If the denominators are different, first change the fractions so they have the same denominator. This is called finding a common denominator.

To change a fraction without changing its value, multiply the top and bottom by the same number. For example, 1/3 = 2/6 = 4/12. These are equivalent fractions.

Worked examples

Example 1: same denominator

Work out 2/7 + 3/7.

The pieces are already the same size (sevenths).

Add the numerators: 2 + 3 = 5
Keep the denominator: 7

Answer: 5/7

Example 2: different denominators

Work out 1/3 + 1/4.

Find the lowest common multiple of 3 and 4. Multiples of 3: 3, 6, 9, 12. Multiples of 4: 4, 8, 12. So the common denominator is 12.
Change each fraction:
- 1/3 = (1 × 4)/(3 × 4) = 4/12
- 1/4 = (1 × 3)/(4 × 3) = 3/12
Add: 4/12 + 3/12 = 7/12

Answer: 7/12. It cannot be simplified, because 7 and 12 share no factor other than 1.

Example 3: subtracting

Work out 5/6 - 3/8.

Lowest common multiple of 6 and 8: multiples of 6 are 6, 12, 18, 24; multiples of 8 are 8, 16, 24. So use 24.
Change each fraction:
- 5/6 = (5 × 4)/(6 × 4) = 20/24
- 3/8 = (3 × 3)/(8 × 3) = 9/24
Subtract: 20/24 - 9/24 = 11/24

Answer: 11/24

Example 4: simplifying the answer

Work out 1/6 + 1/3.

6 is a multiple of 3, so the common denominator is 6.
1/3 = 2/6
1/6 + 2/6 = 3/6
Simplify: 3 and 6 are both divisible by 3, so 3/6 = 1/2

Answer: 1/2

Example 5: mixed numbers

Work out 3 1/4 - 1 2/3.

The safest method is to change mixed numbers into improper fractions first.

3 1/4 = (3 × 4 + 1)/4 = 13/4
1 2/3 = (1 × 3 + 2)/3 = 5/3
Common denominator of 4 and 3 is 12:
- 13/4 = 39/12
- 5/3 = 20/12
Subtract: 39/12 - 20/12 = 19/12
Change back to a mixed number: 19 ÷ 12 = 1 remainder 7, so 19/12 = 1 7/12

Answer: 1 7/12

Adding works the same way. For example, 2 1/2 + 1 2/3 = 5/2 + 5/3 = 15/6 + 10/6 = 25/6 = 4 1/6.

The method in four steps

Step	What to do
1	Change any mixed numbers into improper fractions
2	Find a common denominator (the lowest common multiple is easiest)
3	Rewrite each fraction, then add or subtract the numerators only
4	Simplify, and change back to a mixed number if needed

Common mistakes and how to avoid them

Adding the denominators. 1/3 + 1/4 is not 2/7. A quick sense check catches this: 2/7 is less than 1/3, but you added something to 1/3, so the answer must be bigger. Only the numerators are added.

Changing the bottom but not the top. When 1/3 becomes twelfths, the numerator must be multiplied by 4 as well, giving 4/12. Writing 1/12 changes the value of the fraction completely.

Forgetting to simplify. 3/6 is correct but not finished. Divide the top and bottom by their highest common factor. Many exams expect answers in their simplest form.

Mixed numbers that need borrowing. In 3 1/4 - 1 2/3, subtracting the whole numbers and fractions separately gives 2 and 1/4 - 2/3, which is negative and confusing. Converting to improper fractions first avoids this completely.

Multiplying the denominators when a smaller common denominator exists. This is not wrong, just slower. For 5/6 - 3/8, using 48 instead of 24 still works, but you have bigger numbers to simplify at the end.

Try these

3/5 + 1/5
2/3 + 1/6
7/10 - 1/4
1 3/4 + 2 5/6
4 1/2 - 2 2/3

Answers

Same denominator: 4/5.
2/3 = 4/6, so 4/6 + 1/6 = 5/6.
Common denominator 20: 14/20 - 5/20 = 9/20.
7/4 + 17/6 = 21/12 + 34/12 = 55/12 = 4 7/12.
9/2 - 8/3 = 27/6 - 16/6 = 11/6 = 1 5/6.

Still unsure?

Fractions sit underneath a huge amount of later maths, so it is worth getting them solid now. If they still feel shaky, a Qlive teacher can work through them with you one-to-one, starting with a free assessment that finds the exact gap, whether that is equivalent fractions, times tables or something else. You can read more on our maths page, and when you are ready, try our guide to percentages made simple.