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Mixed Numbers & Improper Fractions (Cambridge (CIE) IGCSE Maths) : Revision Note

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Updated on

Cambridge (CIE) Maths: ExtendedEdexcel Maths A: FoundationEdexcel Maths A (Modular): Higher Unit 1Edexcel Maths A: HigherCambridge (CIE) International Maths: ExtendedCambridge (CIE) International Maths: CoreCambridge (CIE) Maths: Core

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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 Tips and Tricks

  • 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 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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Author
Reviewer
Naomi C

Author: Naomi C

Expertise: Maths Content Creator

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.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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