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First teaching 2023

First exams 2025

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Mixed Numbers & Top Heavy Fractions (CIE IGCSE Maths: Core)

Revision Note

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Naomi C

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Naomi C

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Mixed Numbers & Top Heavy Fractions

What are mixed numbers & top heavy fractions?

  • A mixed number has an integer part and a fraction part
    • 3 3 over 4 has the whole number 3 and the fraction 3 over 4, meaning “three and three quarters”
  • A top heavy fraction is also known as an improper fraction 
  • An improper fraction is a fraction where the numerator is bigger than the denominator
    • 15 over 4 means “fifteen quarters”
  • Any fraction that is greater than 1 can be written as either a mixed number or an equivalent improper fraction

How do I convert a mixed number into an improper fraction?

  • Multiply the integer part by the denominator of the fraction part
    • For example, convert 4 6 over 7 into a top heavy fraction
    • 4 cross times 7 equals 28
  • Add the result to the numerator of the fraction part
    • 28 plus 6 equals 34
  • Write the 'new' numerator over the same denominator and ignore the integer part
    • 4 6 over 7 equals 34 over 7

How do I convert an improper fraction into a mixed number?

  • Divide the numerator by the bottom
    • For example, convert 22 over 3 into a mixed number, 22 divided by 3 equals 7 remainder 1
  • The integer part of the mixed number is the whole number
  • The fraction part is the remainder over the denominator
    • 22 over 3 equals 7 1 third

Examiner Tip

  • The term 'improper fraction' is frequently used in exam papers
    • Make sure you remember that improper fractions are the same as top heavy fractions

Worked example

(a)     Write 5 3 over 4 as an improper fraction.

Multiply the whole number by the denominator, and add to the numerator
Keep the denominator the same

fraction numerator open parentheses 5 cross times 4 space close parentheses plus 3 over denominator 4 end fraction

Simplify

bold 23 over bold 4

 

(b)     Write 17 over 5 as a mixed number.

Divide the top by the bottom

17 ÷ 5 = 3 remainder 2

The final answer is 3, with 2 parts still left over
Leave the 3 as the whole number part and put the 2 over the original denominator of 5

bold 3 bold 2 over bold 5

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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.