Ordering Fractions, Decimals & Percentages

Exam code: 4024

Written by: Ashika|Reviewed by: Caroline Carroll|Updated 2 July 2026

When comparing only fractions, write them over a lowest common denominator
- For $\frac{3}{5}, \frac{1}{2}, \frac{13}{20}, \frac{7}{12}$ , the lowest common denominator is 60
- So change them to $\frac{36}{60}, \frac{30}{60}, \frac{39}{60}, \frac{35}{60}$ and then order them by their numerators
- From smallest to largest: $\frac{30}{60}, \frac{35}{60}, \frac{36}{60}, \frac{39}{60}$
- Rewrite in their original form: $\frac{1}{2}, \frac{7}{12}, \frac{3}{5}, \frac{13}{20}$

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

Rather than just listing values in order, symbols can be used to compare them
- For example, $\frac{1}{4} < \frac{1}{3} < \frac{1}{2}$
Recall that $>$ means greater than and $\geq$ means greater than or equal to
- Similarly, $<$ means less than and $\leq$ means less than or equal to
You may also see $=$ and $\neq$ (which means "not equal to")

Worked example

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

$\frac{1}{3}$ , $\frac{2}{5}$ , $\frac{9}{25}$ , $\frac{4}{15}$

Answer:

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

$\frac{1}{3} = \frac{25}{75}$ $\frac{2}{5} = \frac{30}{75}$ $\frac{9}{25} = \frac{27}{75}$ $\frac{4}{15} = \frac{20}{75}$

Compare and write in order from smallest to largest

$\frac{20}{75}, \frac{25}{75}, \frac{27}{75}, \frac{30}{75}$

Rewrite in their original form

$\frac{4}{15}, \frac{1}{3}, \frac{9}{25}, \frac{2}{5}$

Worked example

Without use of a calculator, write these numbers in the spaces below.

$\frac{7}{8}$ , $\frac{5}{6}$ , $0.8$ , $78 %$

..... < ..... < ..... < .....

Answer:

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

$78 % = 0.78$

Convert $\frac{7}{8}$ to a decimal by either using short division, or halving three times

$\begin{array}{rcl} 7 \div 2 & = & 3.5 \\ 3.5 \div 2 & = & 1.75 \\ 1.75 \div 2 & = & 0.875 \end{array}$
so $\frac{7}{8} = 0.875$

Convert $\frac{5}{6}$ to a decimal by using short division

equation

so $\frac{5}{6} = 0.8333 . . . = 0.8 \dot{3}$

Write them all with 3 decimal places to determine the order

$0.875 0.833 0.800 0.780$

Rewrite the decimals in order

$0.78, 0.8, 0.8 \dot{3}, 0.875$

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

$78 % < 0.8 < \frac{5}{6} < \frac{7}{8}$

Ordering FDP