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Comparing and ordering fractions

Comparing and ordering fractions

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Explainer Video

Tutor: Toby

Summary

Comparing and ordering fractions

In a nutshell

To compare and order fractions you may need to change the fractions so they have a common denominator.  Once you find the common denominator, you can compare the numerators of each fraction to see which is larger.


Procedure

1.
Find the common denominator.  For fractions which are multiples of the same number, this will be the largest denominator.
2.
Multiply up the fraction with the smallest denominator so the fractions have a common denominator.
3.
Compare the numerators of the fractions found in Step Two.  The fraction with the larger numerator is the greater fraction.
Note: Make sure to give your answer as the fraction given in the question.  Do not answer with your 'multiplied up' fraction from Step Two.

Example

Which is larger 78\frac{7}{8}87​ or 34\frac{3}{4}43​?


The common denominator here is the larger denominator:

888​

Multiply up the fraction with the smallest denominator:

3×24×2=68\frac{3\times2}{4\times2}=\frac{6}{8}4×23×2​=86​​​


Compare the numerators of the fractions:

6<76 < 76<7​ therefore 68<78\frac{6}{8}<\frac{7}{8}86​<87​​


Give the answer back into the fraction form given in the question:


34<78\frac{3}{4}<\frac{7}{8}43​<87​​ so 710‾\underline{\frac{7}{10}}107​​ is the larger fraction.

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Learn with Basics

Learn the basics with theory units and practise what you learned with exercise sets!
Length:
Fractions as numbers

Unit 1

Fractions as numbers

Comparing unit fractions

Unit 2

Comparing unit fractions

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Score 80% to jump directly to the final unit.

Optional

Comparing and ordering fractions

Unit 3

Comparing and ordering fractions

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FAQs - Frequently Asked Questions

How should I give my answer when ordering fractions?

Make sure to give your answer as the fraction given in the question. Do not answer with your 'multiplied up' fraction.

How do I compare fractions whose denominators are all multiples of the same number?

1. Find the common denominator. For fractions which are multiples of the same number, this will be the largest denominator. 2. Multiply up the fraction with the smallest denominator so the fractions have a common denominator. 3. Compare the numerators of the fractions found in Step Two. The fraction with the larger numerator is the greater fraction.

What is the common denominator for fractions whose denominators are all multiples of each other?

For fractions which are multiples of the same number, this will be the largest denominator.

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