Mixed numbers | Year 4 | Ascent Library

01 / LEARN

The idea, step by step

Whole groups and a remainder

A mixed number records complete wholes and a leftover fraction. In $2 \frac{1}{3}$ , the 2 counts complete wholes and the one third describes the extra part.

To rename seven thirds, group six thirds into two wholes. One third remains. This gives $\frac{7}{3} = 2 \frac{1}{3}$ .

Count all parts to go the other way

To rename a mixed number as one fraction, count the equal parts inside every whole, then add the leftover parts.

The denominator stays the same. Two and three quarters means two groups of four quarters plus three more quarters, making eleven quarters.

A common trap

Renaming $2 \frac{1}{3}$ as $\frac{3}{3}$ by adding the visible 2 and 1.

Instead: The 2 represents two wholes, so it represents six thirds. Add the one third to get seven thirds.

02 / WORKED EXAMPLES

See the thinking

Example 1

From a fraction

Write $\frac{13}{4}$ as a mixed number.

Twelve quarters make three wholes.
One quarter remains.
Keep the denominator four for the remaining part.

3 \frac{1}{4}

Example 2

From a mixed number

Write $2 \frac{3}{4}$ as one fraction.

Two wholes contain $2 \times 4 = 8$ quarters.
Add the three extra quarters: $8 + 3 = 11$ .

\frac{11}{4}

Check your understanding

What mixed number equals $\frac{5}{2}$ ?

Show answer

$2 \frac{1}{2}$

Four halves make two wholes; one half remains.

03 / WORKSHEET

Your turn

6 questions · 8 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Write $\frac{5}{2}$ as a mixed number.
1 mark
Write $1 \frac{3}{4}$ as quarters.
1 mark
The strips show quarters. Write the total shaded amount as a mixed number.
1 mark
Write $\frac{17}{5}$ as a mixed number.
1 mark
Which is larger, $1 \frac{1}{3}$ or $1 \frac{2}{3}$ ? Explain.
2 marks
A picnic has 3 whole pies and another $\frac{1}{4}$ of an equal-sized pie. How many quarter-pieces is this?
2 marks

Read the worked solutions

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

Write $\frac{5}{2}$ as a mixed number.
1 mark
Group four halves into two wholes; one half remains.
$2 \frac{1}{2}$
Write $1 \frac{3}{4}$ as quarters.
1 mark
One whole is four quarters; four plus three is seven.
$\frac{7}{4}$
The strips show quarters. Write the total shaded amount as a mixed number.
1 mark
Two full strips and one quarter are shaded.
$2 \frac{1}{4}$
Write $\frac{17}{5}$ as a mixed number.
1 mark
Three groups of five fifths use fifteen fifths; two fifths remain.
$3 \frac{2}{5}$
Which is larger, $1 \frac{1}{3}$ or $1 \frac{2}{3}$ ? Explain.
2 marks
The whole-number parts match, so compare one third with two thirds.
$1 \frac{2}{3}$
A picnic has 3 whole pies and another $\frac{1}{4}$ of an equal-sized pie. How many quarter-pieces is this?
2 marks
The three wholes contain twelve quarters; twelve plus one is thirteen.
13 quarter-pieces.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Equivalence; counting beyond one; mixed numbers; number lines.

Official curriculum source ↗

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