Ordering fractions | Year 5

01 / LEARN

The idea, step by step

Compare pieces of the same size

When denominators match, compare numerators: five eighths is more than three eighths. When denominators differ, rename the fractions using equal-sized pieces. For example, $\frac{2}{3} = \frac{8}{12}$ and $\frac{3}{4} = \frac{9}{12}$ , so $\frac{2}{3} < \frac{3}{4}$ .

The larger denominator does not automatically mean the larger fraction. Unit fractions get smaller as a whole is cut into more equal pieces: one eighth is smaller than one fourth.

Use a benchmark to save work

One half is a useful checkpoint. $\frac{3}{8}$ is less than one half because half of eight is four. $\frac{4}{7}$ is greater than one half because four sevenths is more than half of seven sevenths. That proves $\frac{3}{8} < \frac{4}{7}$ without finding a common denominator.

For mixed numbers, compare the whole-number parts first. If those match, compare the fraction parts. A number line should have equal spaces for equal changes; write fractions beside their positions, not in gaps chosen by eye.

A common trap

Saying $\frac{1}{9} > \frac{1}{5}$ because nine is greater than five.

Instead: One ninth uses a smaller share of the same whole. More equal pieces means each piece is smaller.

02 / WORKED EXAMPLES

See the thinking

Example 1

Compare using twelfths

Which is greater: $\frac{5}{6}$ or $\frac{3}{4}$ ?

Rename $\frac{5}{6}$ as $\frac{10}{12}$ .
Rename $\frac{3}{4}$ as $\frac{9}{12}$ .
Ten twelfths is greater than nine twelfths.

\frac{5}{6} > \frac{3}{4}

Example 2

Order amounts around one half

Order $\frac{1}{2}$ , $\frac{3}{8}$ and $\frac{5}{8}$ from smallest to largest.

Rename $\frac{1}{2}$ as $\frac{4}{8}$ .
Compare three eighths, four eighths and five eighths.
Return to the original fraction names.

\frac{3}{8} < \frac{1}{2} < \frac{5}{8}

Check your understanding

Which is smaller: $\frac{2}{5}$ or $\frac{1}{2}$ ?

Show answer

$\frac{2}{5}$

$\frac{2}{5} = \frac{4}{10}$ and $\frac{1}{2} = \frac{5}{10}$ . Four tenths is smaller.

03 / WORKSHEET

Your turn

6 questions · 10 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Insert $<$ , $>$ or $=$ : $\frac{3}{7} ? \frac{5}{7}$ .
1 mark
Insert $<$ , $>$ or $=$ : $\frac{3}{4} ? \frac{6}{8}$ .
1 mark
Which is larger: $\frac{5}{8}$ or $\frac{2}{3}$ ? Show a common denominator.
2 marks
Order $\frac{1}{3}$ , $\frac{5}{6}$ and $\frac{1}{2}$ from smallest to largest.
2 marks
Order $2 \frac{1}{4}$ , $1 \frac{3}{4}$ and $2 \frac{1}{2}$ from smallest to largest.
2 marks
Explain why $\frac{4}{9} < \frac{5}{8}$ using one half as a benchmark.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Insert $<$ , $>$ or $=$ : $\frac{3}{7} ? \frac{5}{7}$ .
1 mark
With the same denominator, compare three and five.
$<$
Insert $<$ , $>$ or $=$ : $\frac{3}{4} ? \frac{6}{8}$ .
1 mark
Multiply the numerator and denominator of three quarters by two.
$=$
Which is larger: $\frac{5}{8}$ or $\frac{2}{3}$ ? Show a common denominator.
2 marks
$\frac{5}{8} = \frac{15}{24}$ and $\frac{2}{3} = \frac{16}{24}$ .
Sixteen twenty-fourths is greater.
$\frac{2}{3}$
Order $\frac{1}{3}$ , $\frac{5}{6}$ and $\frac{1}{2}$ from smallest to largest.
2 marks
In sixths the values are $\frac{2}{6}$ , $\frac{3}{6}$ and $\frac{5}{6}$ .
$\frac{1}{3} < \frac{1}{2} < \frac{5}{6}$
Order $2 \frac{1}{4}$ , $1 \frac{3}{4}$ and $2 \frac{1}{2}$ from smallest to largest.
2 marks
The amount with one whole comes first.
For the two remaining amounts, one quarter is less than one half.
$1 \frac{3}{4} < 2 \frac{1}{4} < 2 \frac{1}{2}$
Explain why $\frac{4}{9} < \frac{5}{8}$ using one half as a benchmark.
2 marks
Half of nine ninths lies between four ninths and five ninths.
Half of eight eighths is four eighths, so five eighths exceeds it.
$\frac{4}{9}$ is below one half and $\frac{5}{8}$ is above one half.

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Curriculum reference & lesson scope

Australian Curriculum v9.0; SA Curriculum Mathematics 2026

Equivalence; mixed numbers; ordering; related-denominator addition/subtraction.

Official curriculum source ↗

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