Syllabus Edition

First teaching 2021

Last exams 2024

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Adding & Subtracting Fractions (CIE IGCSE Maths: Core)

Revision Note

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Adding & Subtracting Fractions

Dealing with mixed numbers

  • Always turn mixed numbers into top heavy fractions before adding or subtracting

Adding & subtracting

  • Adding and subtracting are treated in exactly the same way:
    • Find the lowest common denominator (the smallest whole number that each denominator divides)
    • Write each fraction as an equivalent fraction over this denominator (by multiplying top-and-bottom by the same amount)
    • Add (or subtract) the numerators and write this over a single lowest common denominator
      • do not add the denominators
    • Check for any cancellation (or if asked to turn top heavy fractions back into mixed numbers)

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 divides both 3 and 5

the lowest common denominator is 15
 

Write both fractions as equivalent fractions over 15 (by multiplying top and bottom by the same amount)
 

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 is no cancellation

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 a top heavy fraction (by multiplying the denominator, 4, by the whole number, 3, then adding the numerator, 3)
 

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

To find 15 over 4 minus 5 over 8 first find the lowest common denominator of 4 and 8
 

8 is the smallest number that divides both 4 and 8

the lowest common denominator is 8
 

Write both fractions as equivalent fractions over 8 (by multiplying top and bottom by the same amount)
 

fraction numerator 15 cross times 2 over denominator 4 cross times 2 end fraction minus fraction numerator 5 cross times 1 over denominator 8 cross times 1 end fraction
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 (by dividing 25 by 8 to get 3 remainder 1)
 

equals 3 1 over 8

There is no more cancellation

bold 3 bold 1 over bold 8

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Mark

Author: Mark

Expertise: Maths

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.