National 5MathsSQARevision NotesNumerical SkillsFractionsAddition & Subtraction with Fractions

Addition & Subtraction with Fractions (SQA National 5 Maths): Revision Note

Exam code: X847 75

Roger B

Written by: Roger B

Reviewed by: Dan Finlay

Updated on

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

    • Find the lowest common denominator

    • Write each fraction as an equivalent fraction over this denominator

    • Add (or subtract) the numerators and write this over a single denominator

      • Do not add (or subtract) the denominators

    • Simplify the fraction by cancelling common factors

Examiner Tips and Tricks

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

What do I do if any of the fractions are mixed numbers?

  • Convert any mixed numbers into improper fractions

    • Add or subtract the fractions as usual

    • Remember to convert the answer back to a mixed number if required

Worked Example

(a) Evaluate 3 1 third plus 3 over 5.

(b) Evaluate 5 1 fourth minus 5 over 8.

Answer:

Part (a)

Change 3 1 third into an improper fraction

  • Multiply the denominator by the whole part and add to the numerator

  • Write this value over the denominator

3 1 third equals fraction numerator 3 cross times 3 plus 1 over denominator 3 end fraction equals 10 over 3

So

3 1 third plus 3 over 5 equals 10 over 3 plus 3 over 5

Find the lowest common denominator of 3 and 5

  • 15 is the smallest number that can be divided by both 3 and 5

The lowest common denominator is 15

Write both fractions as equivalent fractions with a common denominator of 15

  • Multiply the numerator and denominator of the first fraction by 5

  • Multiply the numerator and denominator of the second fraction by 3

fraction numerator 10 cross times 5 over denominator 3 cross times 5 end fraction plus fraction numerator 3 cross times 3 over denominator 5 cross times 3 end fraction equals 50 over 15 plus 9 over 15 

Add the numerators and write over a single denominator

fraction numerator 50 plus 9 over denominator 15 end fraction equals 59 over 15 

The question does not specify a form for the answer, so you can give it as either that improper fraction, or as a mixed number

59 over 15 space space open parentheses or space space 3 14 over 15 close parentheses

Part (b)

Change 5 1 fourth into an improper fraction

  • Multiply the denominator by the whole part and add to the numerator

  • Write this value over the denominator

5 1 fourth equals fraction numerator 5 cross times 4 plus 1 over denominator 4 end fraction equals 21 over 4 

So

5 1 fourth minus 5 over 8 equals 21 over 4 minus 5 over 8

Find the lowest common denominator of 4 and 8

  • 8 is the smallest number that by divided by both 4 and 8

The lowest common denominator is 8

Write both fractions as equivalent fractions over 8

  • Multiply the numerator and denominator of the first fraction by 2

fraction numerator 21 cross times 2 over denominator 4 cross times 2 end fraction minus 5 over 8 equals 42 over 8 minus 5 over 8

Subtract the numerators and write over a single denominator

fraction numerator 42 minus 5 over denominator 8 end fraction equals 37 over 8

The question does not specify a form for the answer, so you can give it as either that improper fraction, or as a mixed number

37 over 8 space space open parentheses or space space 4 5 over 8 close parentheses

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    Author
    Reviewer
    Roger B

    Author: Roger B

    Expertise: Maths Content Creator

    Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.

    Dan Finlay

    Reviewer: Dan Finlay

    Expertise: Maths Subject Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.