Mixed numbers | Year 5 | Ascent Library

01 / LEARN

The idea, step by step

Count complete wholes first

An improper fraction has a numerator at least as large as its denominator. It can show one whole or more. For $\frac{11}{4}$ , group the quarters into complete sets of four. Two sets use eight quarters, leaving three quarters. So $\frac{11}{4} = 2 \frac{3}{4}$ .

A mixed number joins a whole-number part with a proper fraction. The denominator still names the size of each fraction piece. Do not change quarters into thirds just because three pieces remain.

Use multiplication to count all pieces

To write $3 \frac{2}{5}$ as fifths, first count the fifths in three wholes: $3 \times 5 = 15$ . Add the extra two fifths, giving $\frac{17}{5}$ .

To reverse the process, divide the numerator by the denominator. The quotient counts complete wholes and the remainder counts the extra pieces. Always keep the original denominator, then simplify the fractional part if needed.

3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{17}{5}

A common trap

Writing $2 \frac{1}{3}$ as $\frac{3}{3}$ by adding two and one.

Instead: Two wholes contain six thirds. Adding the extra third gives seven thirds.

02 / WORKED EXAMPLES

See the thinking

Example 1

Convert a mixed length

Write $2 \frac{5}{6}$ metres as an improper fraction.

Two whole metres contain twelve sixths.
Add the extra five sixths: twelve plus five is seventeen.
Keep sixths as the fraction unit.

\frac{17}{6}

metres.

Example 2

Share an improper amount into wholes

Write $\frac{17}{5}$ as a mixed number.

Seventeen divided by five is three remainder two.
Three groups of five fifths make three wholes.
The two remaining pieces are two fifths.

3 \frac{2}{5}

Check your understanding

Write $\frac{9}{4}$ as a mixed number.

Show answer

$2 \frac{1}{4}$

Eight quarters make two wholes; one quarter remains.

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Write $1 \frac{3}{4}$ as an improper fraction.
1 mark
Write $4 \frac{1}{2}$ as an improper fraction.
1 mark
Write $\frac{14}{3}$ as a mixed number.
2 marks
Write $\frac{19}{6}$ as a mixed number.
2 marks
Write the shaded amount as a mixed number and an improper fraction.
2 marks
Jai has $\frac{13}{4}$ litres of water. Does Jai have more or less than three litres? Explain.
2 marks

Read the worked solutions

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

Write $1 \frac{3}{4}$ as an improper fraction.
1 mark
One whole is four quarters; four plus three is seven.
$\frac{7}{4}$
Write $4 \frac{1}{2}$ as an improper fraction.
1 mark
Four wholes are eight halves; add the extra half.
$\frac{9}{2}$
Write $\frac{14}{3}$ as a mixed number.
2 marks
Four groups of three use twelve thirds. Two thirds remain.
$4 \frac{2}{3}$
Write $\frac{19}{6}$ as a mixed number.
2 marks
Three whole groups use eighteen sixths; one sixth remains.
$3 \frac{1}{6}$
Write the shaded amount as a mixed number and an improper fraction.
2 marks
Two complete bars make ten fifths. The last bar adds two fifths.
$2 \frac{2}{5} = \frac{12}{5}$
Jai has $\frac{13}{4}$ litres of water. Does Jai have more or less than three litres? Explain.
2 marks
Three litres is $\frac{12}{4}$ litres.
$\frac{13}{4} = 3 \frac{1}{4}$ , so it is a quarter of a litre more.
More by one quarter of a litre.

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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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