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IGCSEMathsEdexcelMaths AFoundationRevision Notes1. Numbers & the Number SystemFractions, Decimals & PercentagesOrdering Fractions, Decimals & Percentages

Ordering Fractions, Decimals & Percentages (Edexcel IGCSE Maths A) : Revision Note

Jamie Wood

Written by: Jamie Wood

Reviewed by: Dan Finlay

Updated on

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

Ordering FDP

How do I put fractions in order of size?

  • When comparing only fractions, write them over a lowest common denominator

    • For 3 over 5 comma 1 half comma fraction numerator 13 space over denominator 20 end fraction comma 7 over 12, the lowest common denominator is 60

    • So change them to 36 over 60 comma 30 over 60 comma 39 over 60 comma 35 over 60 and then order them by their numerators

    • From smallest to largest: 30 over 60 comma 35 over 60 comma 36 over 60 comma 39 over 60

    • Rewrite in their original form: 1 half comma 7 over 12 comma 3 over 5 comma 13 over 20

  • Alternatively, a calculator can be used to convert each fraction to a decimal

    • To do this, enter each fraction as a division

How do I put fractions, decimals and percentages in order of size?

  • When comparing a mixture of fractions, decimals and percentages, change everything into decimals

Ordering fractions, decimals, and percentages
Order by Size Notes fig5 (2)
Order by Size Notes fig5 (3)

Which symbols can I use?

  • Rather than just listing values in order, symbols can be used to compare them

    • For example, 1 fourth less than 1 third less than 1 half

  • Recall that greater than means greater than and greater or equal than means greater than or equal to

    • Similarly, less than means less than and less or equal than means less than or equal to

  • You may also see equalsand not equal to (which means "not equal to")

Examiner Tips and Tricks

A calculator can be used to quickly convert any quantities into decimals.

E.g. A fraction can be entered as a division.

Worked Example

Without use of a calculator, write these numbers in order, starting with the smallest.

 1 third 2 over 5 9 over 25 4 over 15

As they are all fractions, write them with a common denominator
The lowest common denominator is be 75
Rewrite each fraction with a denominator of 75

 1 third equals 25 over 75 2 over 5 equals 30 over 75 9 over 25 equals 27 over 75 4 over 15 equals 20 over 75

Compare and write in order from smallest to largest

20 over 75 comma space 25 over 75 comma space 27 over 75 comma space 30 over 75

Rewrite in their original form

bold 4 over bold 15 bold comma bold space bold 1 over bold 3 bold comma bold space bold 9 over bold 25 bold comma bold space bold 2 over bold 5

Worked Example

Write these numbers in the spaces below.

7 over 8 5 over 6 0.8 78 percent sign

..... < ..... < ..... < ..... 

As there is a mixture of fractions, decimals, and percentages, rewrite each as a decimal

0.8 is already a decimal

Convert 78% to a decimal by dividing by 100

78 percent sign space equals space 0.78

Convert 7 over 8 to a decimal by entering into a calculator as a division

7 over 8 equals 7 divided by 8 equals 0.875

Convert 5 over 6 to a decimal in the same way

5 over 6 equals 5 divided by 6 equals 0.8333... equals 0.8 3 with dot on top

Write them all with 3 decimal places to determine the order

0.875 0.833 0.800 0.780

Rewrite the decimals in order

0.78 comma space 0.8 comma space 0.8 3 with dot on top comma space 0.875

Rewrite in their original form, and recall that < means "less than", so the smallest value will be first

bold 78 bold percent sign bold space bold less than bold space bold 0 bold. bold 8 bold space bold less than bold space bold 5 over bold 6 bold space bold less than bold space bold 7 over bold 8

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    Author
    Reviewer
    Jamie Wood

    Author: Jamie Wood

    Expertise: Maths Content Creator

    Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

    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.