Basic Fractions (AQA GCSE Maths) : Revision Note

Basic Fractions

What is a fraction?

• A fraction is part of a whole

• A fraction is written as  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, means that the whole is divided into 3 parts and you have 2 of these parts

How do I find a fraction of an amount?

• Method 1
  Divide by the denominator and multiply by the numerator

  • To find of , divide it by 5 then multiply it by 2

    • , then 

• Method 2
  Change the fraction into a decimal, then multiply

  • To find of , turn into  then multiply

    •  

• Method 3
  Write both numbers as fractions and multiply the two fractions together

  • To find  of , turn into

    • Work out 

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,  and  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

  • is equivalent to  and and etc.

  • For each fraction, there are an infinite number of equivalent 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