Equivalent fractions | Year 4

01 / LEARN

The idea, step by step

Same whole, different partitions

The denominator tells how many equal parts make one whole. The numerator counts the chosen parts. Two fractions are equivalent when they cover the same amount of the same whole.

Splitting every part into smaller equal parts changes both counts. For example, each half can be split into three sixths, so one half is three sixths. The shaded length has not grown.

Rename without changing the amount

Multiply the numerator and denominator by the same positive whole number to make smaller pieces. Divide both by the same non-zero common factor when equal pieces can be grouped together.

Check with a strip or number line. Multiplying only the top changes the amount; multiplying only the bottom changes the piece size without changing how many pieces you chose.

\frac{1}{2} = \frac{3}{6}

A common trap

Changing $\frac{1}{2}$ to $\frac{1}{4}$ by changing only the denominator.

Instead: If each half is split in two, count two quarters for the same half. Change both numerator and denominator.

02 / WORKED EXAMPLES

See the thinking

Example 1

Make sixths

Rename $\frac{2}{3}$ using sixths.

Each third splits into two sixths.
Two thirds contain $2 \times 2 = 4$ sixths.
The whole contains $3 \times 2 = 6$ sixths.

\frac{2}{3} = \frac{4}{6}

Example 2

Group smaller pieces

A ribbon has 4 of its 12 equal sections coloured. What fraction is coloured in thirds?

Group the twelve sections into three equal groups of four.
The four coloured sections fill one of these three groups.
Dividing both 4 and 12 by 4 gives 1 and 3.

\frac{4}{12} = \frac{1}{3}

Check your understanding

Is $\frac{3}{4}$ equivalent to $\frac{6}{8}$ ?

Show answer

Yes.

Each fourth splits into two eighths, so three fourths cover six eighths.

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Write the fraction shaded in the strip.
1 mark
Fill the missing numerator: $\frac{1}{3} = \frac{□}{12}$ .
1 mark
Rename $\frac{2}{5}$ in tenths.
1 mark
Write $\frac{4}{8}$ using halves.
1 mark
Which is equivalent to $\frac{2}{3}$ : $\frac{3}{6}$ or $\frac{4}{6}$ ? Explain.
2 marks
Mia colours $\frac{3}{4}$ of a strip. Leo colours $\frac{6}{8}$ of an equal-length strip. Who colours more? Explain.
2 marks

Read the worked solutions

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

Write the fraction shaded in the strip.
1 mark
There are four equal parts and three are shaded.
$\frac{3}{4}$
Fill the missing numerator: $\frac{1}{3} = \frac{□}{12}$ .
1 mark
The denominator is multiplied by 4, so multiply the numerator by 4.
4
Rename $\frac{2}{5}$ in tenths.
1 mark
Multiply both 2 and 5 by 2.
$\frac{4}{10}$
Write $\frac{4}{8}$ using halves.
1 mark
Divide both numerator and denominator by 4.
$\frac{1}{2}$
Which is equivalent to $\frac{2}{3}$ : $\frac{3}{6}$ or $\frac{4}{6}$ ? Explain.
2 marks
Each third is two sixths, so two thirds are four sixths.
$\frac{4}{6}$
Mia colours $\frac{3}{4}$ of a strip. Leo colours $\frac{6}{8}$ of an equal-length strip. Who colours more? Explain.
2 marks
$\frac{3}{4} = \frac{6}{8}$ ; the wholes have the same length.
They colour equal lengths.

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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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