Ordering fractions | Year 5

01 / LEARN

Understand the idea.

Compare pieces of the same size

Fractions with a common denominator count equal-sized pieces, so compare their numerators. If denominators differ, rename both fractions with a common denominator first. For $\frac{2}{3}$ and $\frac{3}{4}$ , twelfths give $\frac{8}{12}$ and $\frac{9}{12}$ , making the comparison clear.

A larger denominator alone does not mean a larger fraction. For the same whole, cutting it into more pieces makes each piece smaller. With equal numerators, $\frac{1}{8} < \frac{1}{4}$ because an eighth is smaller than a quarter.

Use a benchmark to save work

A benchmark can avoid extra calculation. Since $\frac{3}{8} < \frac{1}{2}$ and $\frac{4}{7} > \frac{1}{2}$ , we know $\frac{3}{8} < \frac{4}{7}$ . Explain which side of the benchmark each fraction lies on; an approximate sketch alone may hide a close comparison.

For mixed numbers with proper fraction parts, compare the whole-number parts first. If they match, compare the fractions. On a number line, equal distances must show equal changes, so use equivalent fractions to place points accurately.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Compare using twelfths

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

Worked solution

1
Rename five sixths as twelfths.
$\frac{5}{6} = \frac{10}{12}$
Multiplying both numbers by 2 preserves the fraction and gives a common unit.
2
Rename three quarters as twelfths.
$\frac{3}{4} = \frac{9}{12}$
Multiplying both numbers by 3 gives the same-sized pieces.
3
Compare the numbers of twelfths.
$\frac{10}{12} > \frac{9}{12}$
Ten equal pieces are more than nine pieces of the same size.
4
State the comparison in the original names.
$\frac{5}{6} > \frac{3}{4}$
Equivalent names preserve the ordering of the original fractions.

Answer

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

EXAMPLE 02

Order amounts around one half

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

Worked solution

1
Rename the half using eighths.
$\frac{1}{2} = \frac{4}{8}$
All three fractions can now be compared in pieces of the same size.
2
Order the numbers of eighths.
$\frac{3}{8} < \frac{4}{8} < \frac{5}{8}$
With equal denominators, the numerators determine the order.
3
Use the original names in the answer.
$\frac{3}{8} < \frac{1}{2} < \frac{5}{8}$
Four eighths and one half name the same point on the number line.

Answer

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

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

$\frac{2}{5}$

Rename both in tenths: $\frac{2}{5} = \frac{4}{10}$ and $\frac{1}{2} = \frac{5}{10}$ . Four tenths is less than five tenths, so $\frac{2}{5}$ is smaller.

Keep practising

6 worksheet questions · 10 marks

Open worksheet 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 ↗

In this lesson

Understand the idea.

Compare pieces of the same size

Use a benchmark to save work

See the method in action.

Compare using twelfths

Rename five sixths as twelfths.

Rename three quarters as twelfths.

Compare the numbers of twelfths.

State the comparison in the original names.

Order amounts around one half

Rename the half using eighths.

Order the numbers of eighths.

Use the original names in the answer.

Try it yourself.

Check your understanding

Keep practising