Basic Fractions (AQA GCSE Maths)

What is a fraction?

• A fraction is part of a whole
• A fraction is written as  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
•  means split something into b parts and take a of them
•  means split something into 2 parts and take 1 of these parts
•  means split the something into 3 parts and take 2 of these parts
•  means split something into 5 parts and take 4 of these parts

How do I find equivalent fractions?

• “Splitting something into 2 parts and taking 1 of these parts” gives the same overall amount as “splitting something into 4 parts and taking 2 of these parts”
  •  is the same as  
  • Using the same idea,  is the same as , or  , or  etc
• Equivalent fractions are two fractions that represent the same amount (they are different ways of writing the same thing)
• To make equivalent fractions, multiply the top and bottom of a fraction by the same amount
  •  is equivalent to  and  and  …etc
  • For each fraction, there are an infinite number of equivalent fractions
• To cancel a fraction down to its “simplest” equivalent form, divide the top and bottom of a fraction by the biggest whole number that goes into both (“common factor”)
  • 
  • 

How do I find a fraction of an amount?

• Method 1: divide by the denominator and multiply by the numerator
  
  • To find  of an amount, divide it by 2
  • To find  of an amount, divide it by 3
  • To find  of an amount, divide it by 5 then multiply it by 2
    •  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  of an amount, multiply the amount by 0.25
  • To find  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 of 60, work out 
  • To find  of , work out 

What are mixed numbers & top heavy fractions?

• A mixed number has a whole number (integer) part and a fraction part

  eg.  has the whole number 3 and the fraction , meaning “three and three quarters”

• A top heavy fraction – also called an improper fraction – is one with the top (numerator) bigger than the bottom (denominator)

  eg.  means “fifteen quarters”

Turning mixed numbers into top heavy fractions

1. Multiply the whole number by the denominator (big × bottom)
2. Add that value to the numerator 
3. Write the "new" numerator over the same denominator as before 

Turning top heavy fractions into mixed numbers

• Divide the top by the bottom (to get a whole number and a remainder)
• The whole number is the big number
• The fraction part is the remainder over the denominator