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Fractions (Cambridge O Level Maths)

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Mark

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Mark

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Introduction to Fractions

What is a fraction?

  • A fraction is part of a whole
  • A fraction is written as a over b where a and b are whole numbers (integers)
    • The number on the top, a, is called the numerator
    • The number on the bottom, b, is called the denominator
  • a over b means split something into b parts and take a of them
    • 1 half means split something into 2 parts and take 1 of these parts
    • 2 over 3 means split the something into 3 parts and take 2 of these parts
    • 4 over 5 means split something into 5 parts and take 4 of these parts

How do I shade a fraction on a diagram?

  • Divide by the denominator and multiply by the numerator
  • To shade 3 over 5 of a grid of 20 squares...
    • first divide 20 squares by 5 to get 4 squares
    • then multiply this amount by 3 to get 12 squares - this is how many to shade
  • Sometimes it will be obvious as the grid will be organised into the number of rows or columns given on the denominator
    • For example, to shade 3 over 5 of a grid of 20 squares, when the grid is in 4 rows of 5, shade 3 of the rows of 5 squares
  • To shade 1 fourth of a circle...
    • divide the circle into four quarters (like sharing a pizza equally between four people)
    • then shade one of these quarters

Worked example

Shade 5 over 7 of the grid below.

             
             
             

 

 

Count the total number of squares in the grid
 

total of 21 squares
 

Divide 21 by 7
 

 21 ÷ 7 = 3 squares
 

Then multiply by 5
 

3 × 5 = 15 squares
 

Shade 15 squares
 

             
             
             

It doesn't matter which 15 you shade, but it's neater to group them together

Fractions of Amounts

How do I find a fraction of an amount?

  • Method 1: divide by the denominator and multiply by the numerator
    • To find 1 half of an amount, divide it by 2
    • To find 1 third of an amount, divide it by 3
    • To find 2 over 5 of an amount, divide it by 5 then multiply it by 2
      • 2 over 5 of 60: do 60 ÷ 5 = 12, then 12 × 2 = 24
  • Method 2 (if you know how to change fractions into decimals): change the fraction into a decimal, then multiply
    • To find 1 fourth of an amount, multiply the amount by 0.25
    • To find 9 over 10 of an amount, multiply the amount by 0.9
  • Method 3 (if you know how to multiply fractions): write both numbers as fractions and multiply two fractions together
    • To find 2 over 3 of 60, work out 2 over 3 cross times 60 over 1
    • To find 5 over 6 of 8 over 3, work out 5 over 6 cross times 8 over 3

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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.