Basic Fractions (Edexcel GCSE Maths: Foundation)

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Naomi C

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Naomi C

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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 integers
    • The number on the top, a, is called the numerator
    • The number on the bottom, b, is called the denominator
  • The values of the numerator and denominator tell us about the size of the fraction 
    • The denominator is how many parts the whole is split into 
    • The numerator is how many parts you have
      • For example, 2 over 3 means that the whole is divided into 3 parts and you have 2 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
      • Divide 20 squares by 5 to get 4 squares
      • Multiply this amount by 3 to get 12 squares 
      • Shade 12 squares
    • To shade 1 fourth of a circle
      • Divide the circle into four quarters by drawing a horizontal and a vertical line through the centre
      • 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
 

Multiply by 5
 

3 × 5 = 15
 

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 third of 90, divide it by 3
      • 90 divided by 3 equals 30
    • To find 2 over 5 of 60, divide it by 5 then multiply it by 2
      • 60 divided by 5 equals 12, then 12 cross times 2 equals 24
  • Method 2
    Change the fraction into a decimal, then multiply
    • To find 1 fourth of 16, turn 1 fourth into 0.25 then multiply
      •  0.25 cross times 16 equals 4
    • To find 9 over 10 of 15, turn 9 over 10 into 0.9 then multiply
      •  0.9 cross times 15 equals 13.5
  • Method 3
    Write both numbers as fractions and multiply two fractions together
    • To find 2 over 3 of 60, write 60 as 60 over 1
      • work out 2 over 3 cross times 60 over 1 equals 120 over 3 equals 40
    • To find 5 over 6 of 8 over 3
        • work out 5 over 6 cross times 8 over 3 equals 40 over 18 equals 20 over 9

Equivalent Fractions

What are equivalent fractions?

  • Equivalent fractions are two fractions that represent the same amount
    • They are different ways of writing the same thing
    • For example, 1 half and 6 over 12 are equivalent fractions

How do I find an equivalent fraction?

  • To find an equivalent fraction, multiply the top and bottom of a fraction by the same number
    • 5 over 6 is equivalent to fraction numerator 5 cross times 2 over denominator 6 cross times 2 end fraction equals 10 over 12 and fraction numerator 5 cross times 3 over denominator 6 cross times 3 end fraction equals 15 over 18 and fraction numerator 5 cross times 4 over denominator 6 cross times 4 end fraction equals 20 over 24etc.
    • For each fraction, there are an infinite number of equivalent fractions

Examiner Tip

  • Using equivalent fractions can help with shading parts of diagrams questions as well as adding and subtracting fractions without a calculator.
    • Remember that if you have your calculator in the exam you can use it to check your work.

Simplifying Fractions

What is a simplified fraction?

  • A simplified fraction is a fraction that is written using the smallest possible integer values
    • Simplifying turns a fraction into an 'easier' equivalent fraction
  • If both the numerator and denominator can be divided by the same number (called a common factor), the fraction can be simplified
  • Simplifying is also called cancelling a fraction

How do I simplify fractions?

  • To simplify the fraction, divide the top and bottom by the common factor
    • 12 over 18 equals fraction numerator 12 divided by 6 over denominator 18 divided by 6 end fraction equals 2 over 3
    • 25 over 45 equals fraction numerator 25 divided by 5 over denominator 45 divided by 5 end fraction equals 5 over 9

Examiner Tip

  • Make use of your calculator if you have it in your exam.
    • Type any fraction into it and pressing equals will automatically simplify the fraction for you.
    • If the question asks you to show your working, you must show which number you divided by.

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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.