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Adding & Subtracting Fractions (Edexcel GCSE Maths)

Revision Note

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Edexcel Maths: FoundationEdexcel Maths: Higher

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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 the denominators

    • Simplify the fraction by cancelling common factors

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) Find 2 over 3 plus 1 fifth.

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 2 cross times 5 over denominator 3 cross times 5 end fraction plus fraction numerator 1 cross times 3 over denominator 5 cross times 3 end fraction equals 10 over 15 plus 3 over 15 

Add the numerators and write over a single denominator

fraction numerator 10 plus 3 over denominator 15 end fraction equals 13 over 15 

There are no common factors that will cancel

bold 13 over bold 15

(b) Find 3 3 over 4 minus 5 over 8 giving your answer as a mixed number.

Change the mixed number into an improper fraction

Multiply the denominator by the whole part and add to the numerator
Write this value over the denominator

fraction numerator 4 cross times 3 plus 3 over denominator 4 end fraction equals 15 over 4 

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 15 cross times 2 over denominator 4 cross times 2 end fraction minus 5 over 8 equals 30 over 8 minus 5 over 8

Subtract the numerators and write over a single denominator

fraction numerator 30 minus 5 over denominator 8 end fraction equals 25 over 8

Change into a mixed number
Divide 25 by 8 to get 3 remainder 1

bold 3 bold 1 over bold 8

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    Previous:Mixed Numbers & Improper FractionsNext:Multiplying & Dividing Fractions
    Author
    Reviewer
    Naomi C

    Author: Naomi C

    Expertise: Maths

    Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths 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.