Mixed numbers | Year 4 | Ascent Library

01 / LEARN

Understand the idea.

Whole groups and a remainder

A mixed number records whole units plus a fraction of another unit. In $2 \frac{1}{3}$ , the $2$ means two complete wholes and $\frac{1}{3}$ means one extra third. It does not mean two times one third.

To rename $\frac{7}{3}$ , make groups of three thirds. Six thirds make two complete wholes, leaving one third. The two names $\frac{7}{3}$ and $2 \frac{1}{3}$ describe the same point on a number line.

Count all parts to go the other way

To turn a mixed number into one fraction, count how many pieces fit in each whole. In $2 \frac{3}{4}$ , two wholes contain eight quarters. Include the three extra quarters to count eleven quarters altogether.

The denominator stays the same because the pieces are still quarters. A useful check is to regroup the final numerator into wholes again. If you recover the original whole-number part and leftover fraction, the two names agree.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

From a fraction

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

Worked solution

1
Find the number of complete wholes.
$13 = 3 \times 4 + 1$
Three groups of four quarters use twelve quarters and leave one.
2
Rename the complete groups.
$\frac{12}{4} = 3$
Four quarters fill each whole, so twelve quarters fill three wholes.
3
Include the leftover quarter.
$\frac{13}{4} = 3 \frac{1}{4}$
The extra piece is still a quarter, so its denominator remains four.

Answer

$3 \frac{1}{4}$

EXAMPLE 02

From a mixed number

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

Worked solution

1
Count the quarters in two wholes.
$2 \times 4 = 8$
Every whole contains four quarters.
2
Add the extra quarters.
$8 + 3 = 11$
The mixed number includes three quarters beyond its two complete wholes.
3
Write all the pieces as one fraction.
$2 \frac{3}{4} = \frac{11}{4}$
Eleven quarter-sized pieces have the same total size as the mixed number.

Answer

$\frac{11}{4}$

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

$2 \frac{1}{2}$

Five halves contain two full pairs of halves and one half left over. Thus $\frac{5}{2} = 2 \frac{1}{2}$ ; the denominator remains two because the pieces are still halves.

Keep practising

6 worksheet questions · 8 marks

Open worksheet 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 ↗

In this lesson

Understand the idea.

Whole groups and a remainder

Count all parts to go the other way

See the method in action.

From a fraction

Find the number of complete wholes.

Rename the complete groups.

Include the leftover quarter.

From a mixed number

Count the quarters in two wholes.

Add the extra quarters.

Write all the pieces as one fraction.

Try it yourself.

Check your understanding

Keep practising