Comparing/ordering | Year 6

01 / LEARN

The idea, step by step

Compare the same-sized parts

When denominators match, the pieces have equal size and the greater numerator gives the greater fraction. With different denominators, first rename the fractions with a common denominator.

For 3/4 and 5/6, twelfths are convenient. Renaming makes the parts directly comparable without changing either amount.

Rename to compare the same whole
Fraction	Equivalent twelfths
3/4	9/12
5/6	10/12

Use benchmarks to check

A fraction below one half has a numerator less than half its denominator. A fraction above one half has a numerator greater than half its denominator. Benchmarks sometimes settle a comparison without a full common-denominator calculation.

For practical quantities, check that the wholes are equal. Fractions of differently sized bottles cannot tell you which contains more water unless you also know the bottle sizes.

A common trap

The fraction with the larger denominator is always greater.

Instead: More equal parts means smaller pieces. One eighth is smaller than one quarter of the same whole.

02 / WORKED EXAMPLES

See the thinking

Example 1

Worked example 1

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

Rename them as 9/12 and 10/12.
Ten twelfths are more than nine twelfths.

\frac{5}{6}

Example 2

Worked example 2

Order $\frac{2}{3}$ , $\frac{1}{4}$ and $\frac{3}{8}$ from least to greatest.

Use twenty-fourths: 16/24, 6/24 and 9/24.
Order the numerators 6, 9, 16.

\frac{1}{4}, \frac{3}{8}, \frac{2}{3}

Check your understanding

Which is greater: $\frac{7}{12}$ or $\frac{1}{2}$ ?

Show answer

$\frac{7}{12}$ .

One half is 6/12, so 7/12 is greater.

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Compare $\frac{3}{8}$ and $\frac{5}{8}$ using < or >.
1 mark
Which is greater: $\frac{2}{3}$ or $\frac{3}{5}$ ?
2 marks
Order $\frac{1}{2}$ , $\frac{3}{4}$ and $\frac{2}{3}$ from least to greatest.
2 marks
Is $\frac{4}{9}$ below or above one half?
1 mark
Give a fraction strictly between $\frac{1}{4}$ and $\frac{3}{4}$ .
2 marks
Identical bottles are filled to $\frac{5}{6}$ and $\frac{7}{8}$ . Which contains more water?
2 marks

Read the worked solutions

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

Compare $\frac{3}{8}$ and $\frac{5}{8}$ using < or >.
1 mark
The pieces have the same size, so compare the numerators.
$\frac{3}{8} < \frac{5}{8}$ .
Which is greater: $\frac{2}{3}$ or $\frac{3}{5}$ ?
2 marks
2/3=10/15 and 3/5=9/15.
$\frac{2}{3}$ .
Order $\frac{1}{2}$ , $\frac{3}{4}$ and $\frac{2}{3}$ from least to greatest.
2 marks
Use twelfths: 6/12, 9/12 and 8/12.
$\frac{1}{2}, \frac{2}{3}, \frac{3}{4}$ .
Is $\frac{4}{9}$ below or above one half?
1 mark
Half of 9 is 4.5; 4 is less than 4.5.
Below.
Give a fraction strictly between $\frac{1}{4}$ and $\frac{3}{4}$ .
2 marks
1/2=2/4 lies between them. Other correct answers are possible.
For example, 1/2.
Identical bottles are filled to $\frac{5}{6}$ and $\frac{7}{8}$ . Which contains more water?
2 marks
5/6=20/24 and 7/8=21/24.
The bottle filled to 7/8.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Equivalence; comparing/ordering; addition/subtraction; practical quantities.

Official curriculum source ↗

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