National 5MathsSQAApplications of MathematicsRevision NotesNumeracy SkillsFractions & PercentagesAddition & Subtraction with Fractions

Addition & Subtraction with Fractions (SQA National 5 Applications of Mathematics): Revision Note

Exam code: X844 75

Written by: Dan Finlay

Reviewed by: Roger B

Updated on 1 December 2025

Adding & subtracting fractions

How do I add or subtract two fractions?

Addition and subtraction are treated in exactly the same way when dealing with fractions

Same denominators

If the denominators are the same:
- Add or subtract the numerators
- Leave the denominator unchanged
For example:
- $\frac{3}{7} + \frac{2}{7} = \frac{5}{7}$
- $\frac{9}{9} - \frac{5}{9} = \frac{4}{9}$

Different denominators

STEP 1
Find a number that is a common multiple of both denominators
- You can multiply the two denominators together
  - e.g. 20 is a common multiple of 5 and 4
STEP 2
Write each fraction as an equivalent fraction using the common multiple as the denominator
- Multiply the numerator and denominator by the same amount
  - e.g. $\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}$ and $\frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}$
STEP 3
Add (or subtract) the numerators and write this over a single denominator
- Do not add (or subtract) the denominators
  - e.g. $\frac{3}{5} + \frac{1}{4} = \frac{12}{20} + \frac{5}{20} = \frac{17}{20}$
STEP 4
Simplify the fraction (if necessary) by cancelling any common factors

Examiner Tips and Tricks

You should be familiar with converting between equivalent fractions from your National 4 course.

How do I subtract a fraction from a whole number?

Write the whole number as an improper fraction using the same denominator as the fraction
- e.g. $2 = \frac{4}{2}$ and $1 = \frac{7}{7}$
You can now subtract the numerators as the denominators are the same
- e.g. $2 - \frac{1}{2} = \frac{4}{2} - \frac{1}{2} = \frac{3}{2}$
- e.g. $1 - \frac{2}{7} = \frac{7}{7} - \frac{2}{7} = \frac{5}{7}$

Examiner Tips and Tricks

There is usually a question on Paper 1 which asks you to add two fractions together and then subtract from a whole number.

Worked Example

George and Sophie share two cakes.

George eats $\frac{3}{4}$ of a cake. Sophie eats $\frac{2}{3}$ of a cake.

Calculate the total amount of cake left over.

Answer:

Method 1

Add together the two fractions

Find a common multiple of the denominators

$4 \times 3 = 12$

Rewrite the fractions using this as the denominator

$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$

$\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$

Add the numerators

$\frac{9}{12} + \frac{8}{12} = \frac{17}{12}$

Write 2 as an improper fraction with 12 as the denominator

There are 12 twelfths in a whole number

$2 = \frac{24}{12}$

Subtract the fractions

$\frac{24}{12} - \frac{17}{12} = \frac{7}{12}$

$\frac{7}{12}$

Method 2

Subtract each fraction from 1

To find the remaining fraction from each cake

$1 - \frac{3}{4} = \frac{4}{4} - \frac{3}{4} = \frac{1}{4}$

$1 - \frac{2}{3} = \frac{3}{3} - \frac{2}{3} = \frac{1}{3}$

Add together the two fractions

Find a common multiple of the denominators

$4 \times 3 = 12$

Rewrite the fractions using this as the denominator

$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$

$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$

Add the numerators

$\frac{3}{12} + \frac{4}{12} = \frac{7}{12}$

$\frac{7}{12}$

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

I would just like to say a massive thank you for putting together such a brilliant, easy to use website.I really think using this site helped me secure my top gradesin science and maths. You really did save my exams! Thank you.

Beth
IGCSE Student

This website is soooo useful and I can’t ever thank you enough for organising questions by topic like this. Furthermore, the name of the website could not have been more appropriate as it literally did SAVE MY EXAMS!

Fathima
A Level Student

Incredible! SO worth my money, the revision notes have everything I need to know and are so easy to understand. I actually enjoy revising! It makes me feel a lot more confident for my GCSEs in a few months.

Kate
GCSE Student

Absolutely brilliant, both my girls used it for A levels and GCSE. It's saves on paper copies, also beneficial exam questions ranked from easy to hard. It's removed a lot of stress from the exams.

Sameera
Parent

Just to say that your resources are the best I have seen and I have been teaching chemistry at different levels for about 40 years

Mark
Chemistry Teacher

Excellent

Addition & Subtraction with Fractions (SQA National 5 Applications of Mathematics): Revision Note

Adding & subtracting fractions

How do I add or subtract two fractions?

Same denominators

Different denominators

Examiner Tips and Tricks

How do I subtract a fraction from a whole number?

Examiner Tips and Tricks

Worked Example

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

Author: Dan Finlay

Reviewer: Roger B