Equivalent fractions | Year 4

01 / LEARN

Understand the idea.

Same whole, different partitions

The denominator names the equal parts in one whole; the numerator counts how many of those parts are chosen. Equivalent fractions name the same amount of the same whole, even when the pieces have different sizes.

Compare the strips: cutting each half into three equal pieces makes sixths. One half now contains three sixths, but the shaded length stays unchanged. Both the total number of pieces and the number of shaded pieces have tripled.

Rename without changing the amount

To make an equivalent fraction with smaller pieces, multiply the numerator and denominator by the same positive whole number. To group pieces into larger equal pieces, divide both by the same common factor. The amount stays unchanged because both counts change together.

Use a strip or number line to check that the renamed fraction reaches the same point. Changing only the numerator changes how much you choose. Changing only the denominator changes the piece size, so it usually changes the amount too.

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

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Make sixths

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

Worked solution

1
Find how thirds become sixths.
$3 \times 2 = 6$
Each third must split into two equal pieces, doubling the number of parts in the whole.
2
Count the smaller pieces in the chosen thirds.
$2 \times 2 = 4$
The two chosen thirds each contain two sixths.
3
Rename both counts together.
$\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$
Four sixths cover the same amount of the whole as two thirds.

Answer

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

EXAMPLE 02

Group smaller pieces

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

Worked solution

1
Write the coloured share.
$\frac{4}{12}$
Four of the twelve equal sections are coloured.
2
Find how many twelfths make a third.
$12 \div 3 = 4$
Splitting twelve sections into three equal amounts gives four sections per third.
3
Group the numerator and denominator by four.
$\frac{4}{12} = \frac{4 \div 4}{12 \div 4} = \frac{1}{3}$
The four coloured sections total one of the three equal shares of the ribbon.

Answer

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

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

Yes.

Yes. Split every fourth in two: $\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$ . Six smaller pieces cover exactly the same amount as three fourths.

Keep practising

6 worksheet questions · 8 marks

Open worksheet 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 ↗

In this lesson

Understand the idea.

Same whole, different partitions

Rename without changing the amount

See the method in action.

Make sixths

Find how thirds become sixths.

Count the smaller pieces in the chosen thirds.

Rename both counts together.

Group smaller pieces

Write the coloured share.

Find how many twelfths make a third.

Group the numerator and denominator by four.

Try it yourself.

Check your understanding

Keep practising