How do I add two fractions? (plus example)

Adding (and subtracting) fractions is more difficult than multiplying them because we need to make sure that the denominators (bottom numbers) are equal in both fractions.

To do this, we may need to change the way we have written the fractions (without actually changing the fractions themselves).

Given the problem

(a/b) + (c/d),

we need to ensure that the denominators are equal.

To do this:

- multiply the top and bottom of the left hand side fraction by b

- multiply the top and bottom of the right hand side fraction by d

(Because we multiply the top AND bottom of the fraction, we essentially still have the same fraction, just written in a different way.)

We now have 

(ad/bd) + (cb/bd).

The denominators are now equal, so we can simply rewrite this as

(ad+cb)/bd, which is our final answer.



Example: Find (3/4) + (2/5).

We need to 

- multiply top and bottom of left fraction by 5

- multiply top and bottom of right fraction by 4

This gives

((3 x 5) / (4 x 5) )    +    ((2 x 4) / (4 x 5))

which is equal to 

(15/20) + (8/20).

We can now add the fractions (only add the top numbers together!) to get the answer,


Jenny B. A Level Maths tutor, GCSE Maths tutor

2 years ago

Answered by Jenny, a GCSE Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


Jed R. GCSE Further Mathematics  tutor, GCSE Maths tutor
View profile
£18 /hr

Jed R.

Degree: Engineering Mathematics (Masters) - Bristol University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“A bit about meI am s student studying engineering mathematics at Bristol University. Maths is a passion of mine and I like to see people who are enthusiastic to learn. While at college I took part in a mentoring scheme where I volu...”

Eleanor B. A Level Biology tutor, GCSE Maths tutor, GCSE Biology tuto...
View profile
£18 /hr

Eleanor B.

Degree: Zoology (Bachelors) - Bristol University

Subjects offered: Maths, Music+ 2 more


“I am currently studying Zoology at the University of Bristol. I have a younger brother who took his GCSE's last year, and I helped him with revision, which made me realise that I really enjoy teaching! I hope that through these sessio...”

PremiumEmma W. Uni Admissions Test .PAT. tutor, GCSE Chemistry tutor, A Leve...
View profile
£30 /hr

Emma W.

Degree: Physics (Bachelors) - Oxford, St Anne's College University

Subjects offered: Maths, Physics+ 2 more

Further Mathematics

“I am friendly and approachable as well as highly organised and reliable, and I am always dedicated to my students- I want you to do well!”

About the author

Jenny B. A Level Maths tutor, GCSE Maths tutor
View profile
£18 /hr

Jenny B.

Degree: Mathematics (Bachelors) - Nottingham University

Subjects offered: Maths


“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Posts by Jenny

How do I add two fractions? (plus example)

How do I expand (x+a)(x+b)? (plus example)

Other GCSE Maths questions

Solve 8(x + 3) = 36

Why maths?

How do you solve a simultaneous equation?

What is Standard form? And when can I use it?

View GCSE Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss