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First teaching 2023

First exams 2025

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Ordering FDP (CIE IGCSE Maths: Core)

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Jamie W

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Jamie W

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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

 

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 Tip

  • A calculator can be used to quickly convert any quantities into decimals
    • However, this type of question will often be in the non-calculator paper

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

Without use of a calculator, 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 either using short division, or halving three times

table row cell 7 divided by 2 end cell equals cell 3.5 end cell row cell 3.5 divided by 2 end cell equals cell 1.75 end cell row cell 1.75 divided by 2 end cell equals cell 0.875 end cell end table
so 7 over 8 equals 0.875

Convert 5 over 6 to a decimal by using short division

so 5 over 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

If a calculator was allowed for this question, it could be used to find 7 divided by 8 and 5 divided by 6 more easily

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Jamie W

Author: Jamie W

Expertise: Maths

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.