IGCSEMathsCambridge (CIE)International MathsExtendedRevision NotesNumberFractionsMixed Numbers & Improper Fractions

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

Exam code: 0607

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Updated on

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

Mixed numbers & improper fractions

What are mixed numbers & improper 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”

  • An improper fraction is also known as a top-heavy 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?

  • Consider 5 2 over 7

  • STEP 1
    Split the whole number into multiples of the denominator

    • 1 whole is equal to 7 sevenths

      Therefore, 5 is equal to 5 × 7 = 35 sevenths

  • STEP 2
    Add the numerator of the fraction part

    • 35 sevenths and 2 sevenths make 37 sevenths

    • 5 2 over 7 equals 37 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

Worked Example

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

Answer:

Split the whole number into quarters

1 whole is 4 quarters

5 wholes is 5 × 4 = 20 quarters

Add the quarters from the fraction

20 + 3 = 23 quarters

23 over 4

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

Answer:

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

3 2 over 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 Subject 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.