Unit fractions | Year 3 | Ascent Library

01 / LEARN

Understand the method.

THE CORE RULE

\frac{1}{6}

One sixth means one of six equal parts.

Start with equal parts

First choose the whole. It might be one strip, one shape or one collection.

Split the whole into equal parts. One of those parts is a unit fraction.

Read the two numbers

In $\frac{1}{6}$ , the 6 counts all the equal parts. The 1 counts the part chosen. Say one sixth.

Two unequal pieces are not halves. The pieces must be the same size.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

One piece of a strip

A strip has 5 equal pieces. One is coloured. What fraction is coloured?

Worked solution

1
Count all the equal pieces.
$5 equal pieces$
The denominator is 5 because five equal pieces make the whole strip.
2
Count the coloured pieces.
$\frac{1}{5}$
One piece is coloured. Write 1 on top and say one fifth.

Answer

$\frac{1}{5}$ , or one fifth.

EXAMPLE 02

Is it a half?

A sandwich is cut into 2 pieces. One piece is much larger. Has each person received one half?

Worked solution

1
Check the sizes of the pieces.
A half is one of two equal parts. These pieces are unequal.

Answer

No. The pieces must be equal to be halves.

03 / YOUR TURN

Try it yourself.

Calculate, explain, then apply.

CHECK 01

Your turn

One whole is shared into 8 equal parts. Name one part.

Show answer & reasoning

One eighth, $\frac{1}{8}$ .

The 8 counts all equal parts. The 1 counts the single part chosen.

Keep practising

6 worksheet questions

Open worksheet Worked solutions

Read the questions online

A strip has 3 equal parts. One is shaded. Write the shaded fraction.
A shape has 10 equal parts. Name one part in words.
What does the 5 mean in $\frac{1}{5}$ ?
Write the coloured fraction in this strip.
A cake is cut into 4 pieces of different sizes. Is every piece one quarter? Explain.
Three children share a ribbon equally. What fraction of the ribbon does each receive?

Read the worked solutions

A strip has 3 equal parts. One is shaded. Write the shaded fraction.
Count 3 equal parts in the whole. Choose 1.
$\frac{1}{3}$ .
A shape has 10 equal parts. Name one part in words.
There are 10 equal parts, so one part is one tenth.
One tenth.
What does the 5 mean in $\frac{1}{5}$ ?
The denominator counts the equal parts of the whole.
Five equal parts make the whole.
Write the coloured fraction in this strip.
There are 4 equal parts and 1 is coloured.
$\frac{1}{4}$ .
A cake is cut into 4 pieces of different sizes. Is every piece one quarter? Explain.
Equal size is needed as well as 4 pieces.
No. Quarters must be 4 equal parts.
Three children share a ribbon equally. What fraction of the ribbon does each receive?
The whole ribbon is divided into 3 equal shares. Each child receives one.
$\frac{1}{3}$ of the ribbon.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Unit fractions; halves/thirds/quarters/fifths/tenths; multiples; completing a whole.

Official curriculum source ↗