Mixed numbers | Year 5 | Ascent Library

01 / LEARN

Understand the idea.

Count complete wholes first

An improper fraction has at least one whole because its numerator is at least its denominator. In $\frac{11}{4}$ , each set of four quarters makes one whole. Eight quarters make two wholes, leaving three quarters: $2 \frac{3}{4}$ .

A mixed number combines whole units and a proper fraction. The denominator still tells the size of the leftover pieces. Three pieces left over do not become thirds if the original pieces were quarters.

Use multiplication to count all pieces

To convert a mixed number into one fraction, count all pieces of the same size. For $3 \frac{2}{5}$ , each whole contains five fifths; three wholes contain $15$ fifths. The extra two give $17$ fifths altogether.

To convert back, divide numerator by denominator. The whole-number quotient counts complete wholes, and the remainder counts leftover pieces. Keep the denominator, simplify the leftover fraction if possible, and check that it is less than one.

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

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Convert a mixed length

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

Worked solution

1
Count the sixths in two whole metres.
$2 \times 6 = 12$
Each whole metre contains six sixths of a metre.
2
Include the extra five sixths.
$12 + 5 = 17$
Whole metres and the fractional part must both be counted in sixths.
3
Write the result with its measurement unit.
$2 \frac{5}{6} m = \frac{17}{6} m$
The denominator remains 6 because the piece size has not changed.

Answer

$\frac{17}{6}$ metres.

EXAMPLE 02

Share an improper amount into wholes

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

Worked solution

1
Group seventeen fifths into complete wholes.
$17 = 5 \times 3 + 2$
Three groups of five fifths make three wholes, leaving two fifths.
2
Write the whole-number and fractional parts.
$\frac{17}{5} = 3 \frac{2}{5}$
The quotient is 3 and the remainder counts 2 pieces of size one fifth.
3
Check by counting the fifths again.
$3 \times 5 + 2 = 17$
The mixed number contains exactly the original seventeen fifths.

Answer

$3 \frac{2}{5}$ .

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

$2 \frac{1}{4}$

$9 = 4 \times 2 + 1$ , so nine quarters contain two whole groups of four quarters and one quarter left. Thus $\frac{9}{4} = 2 \frac{1}{4}$ .

Keep practising

6 worksheet questions · 10 marks

Open worksheet 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 ↗

In this lesson

Understand the idea.

Count complete wholes first

Use multiplication to count all pieces

See the method in action.

Convert a mixed length

Count the sixths in two whole metres.

Include the extra five sixths.

Write the result with its measurement unit.

Share an improper amount into wholes

Group seventeen fifths into complete wholes.

Write the whole-number and fractional parts.

Check by counting the fifths again.

Try it yourself.

Check your understanding

Keep practising