Equivalent fractions | Year 6

01 / LEARN

The idea, step by step

Same amount, more pieces

The denominator names the number of equal parts in one whole. The numerator counts the selected parts. If every part is split in the same way, both counts increase while the selected amount stays unchanged.

For example, splitting every fifth into four pieces changes 3 fifths into 12 twentieths. Multiply the numerator and denominator by the same factor. Multiplying only the numerator would change the amount.

Simplify by joining pieces

Divide the numerator and denominator by a common factor to make an equivalent fraction with fewer parts. Continue until there is no common factor greater than 1.

Keep the whole the same size when comparing diagrams. Half of a large cake and half of a small cake name the same fraction, but not necessarily the same quantity of cake.

A common trap

Adding the same number to a numerator and denominator preserves the fraction.

Instead: Use multiplication or division by the same factor. For example, 1/2 and 3/4 are not equal.

02 / WORKED EXAMPLES

See the thinking

Example 1

Worked example 1

Write $\frac{3}{5}$ with denominator 20.

5×4=20, so each fifth becomes four twentieths.
Multiply the numerator by 4 too: 3×4=12.

\frac{12}{20}

Example 2

Worked example 2

Simplify $\frac{18}{24}$ .

18 and 24 share the factor 6.
18÷6=3 and 24÷6=4.

\frac{3}{4}

Check your understanding

Is $\frac{4}{6}$ equivalent to $\frac{2}{3}$ ?

Show answer

Yes.

Divide the numerator and denominator of 4/6 by 2.

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Complete $\frac{2}{3} = \frac{?}{12}$ .
1 mark
Write $\frac{5}{8}$ with denominator 24.
1 mark
Simplify $\frac{12}{20}$ .
1 mark
Simplify $\frac{21}{28}$ .
1 mark
Write the shaded fraction, then simplify it.
2 marks
Noah says $\frac{2}{5} = \frac{4}{7}$ because he added 2 to both numbers. Explain the error and give an equivalent fraction.
2 marks

Read the worked solutions

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

Complete $\frac{2}{3} = \frac{?}{12}$ .
1 mark
Multiply numerator and denominator by 4.
8.
Write $\frac{5}{8}$ with denominator 24.
1 mark
Multiply both counts by 3.
$\frac{15}{24}$ .
Simplify $\frac{12}{20}$ .
1 mark
Divide both counts by 4.
$\frac{3}{5}$ .
Simplify $\frac{21}{28}$ .
1 mark
Divide both counts by 7.
$\frac{3}{4}$ .
Write the shaded fraction, then simplify it.
2 marks
Six of eight parts are shaded; divide both counts by 2.
$\frac{6}{8} = \frac{3}{4}$ .
Noah says $\frac{2}{5} = \frac{4}{7}$ because he added 2 to both numbers. Explain the error and give an equivalent fraction.
2 marks
Multiply both numerator and denominator by 2 instead.
The amounts differ; one correct equivalent is 4/10.

Checking saved progress…

Continue learning

Comparing/ordering

Next lesson

Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Equivalence; comparing/ordering; addition/subtraction; practical quantities.

Official curriculum source ↗

Back to Fractions