Equivalent fractions | Year 5

01 / LEARN

The idea, step by step

Different names, same share

A fraction compares a number of selected parts with the equal parts in one whole. If we cut each third into two equal pieces, the whole has six pieces. The same shaded amount changes from $\frac{2}{3}$ to $\frac{4}{6}$ . It has not grown. We have changed the size and number of the pieces.

Compare models using the same-sized whole. Two shaded pieces of a small bar and two shaded pieces of a large bar do not necessarily show equal amounts.

Scale both numbers together

Multiply the numerator and denominator by the same non-zero whole number to make an equivalent fraction. For example, $\frac{3}{5} = \frac{6}{10}$ because both numbers were doubled. To simplify, divide both by a common factor.

Keep dividing while the numerator and denominator have a common factor greater than one. In $\frac{8}{12}$ , both are divisible by four, so $\frac{8}{12} = \frac{2}{3}$ . This is simplest form. A quick check is to scale back and recover the original fraction.

\frac{2}{3} = \frac{4}{6} = \frac{8}{12}

A common trap

Multiplying only the denominator makes an equivalent fraction.

Instead: Both numbers must change by the same factor. $\frac{1}{2}$ is not $\frac{1}{6}$ ; $\frac{1}{2} = \frac{3}{6}$ .

02 / WORKED EXAMPLES

See the thinking

Example 1

Make sixths into eighteenths

Complete $\frac{5}{6} = \frac{?}{18}$ .

Six was multiplied by three to make eighteen.
Multiply the numerator by the same three.
Five times three is fifteen.

\frac{5}{6} = \frac{15}{18}

Example 2

Simplify a set of counters

Twelve of eighteen counters are blue. Write the blue fraction in simplest form.

The fraction is $\frac{12}{18}$ .
The greatest common factor of twelve and eighteen is six.
Divide both numbers by six.

\frac{12}{18} = \frac{2}{3}

of the counters are blue.

Check your understanding

Is $\frac{3}{4}$ equivalent to $\frac{9}{12}$ ? Explain.

Show answer

Yes.

Multiplying both three and four by three gives nine and twelve. The selected share stays the same.

03 / WORKSHEET

Your turn

6 questions · 10 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Complete $\frac{1}{2} = \frac{?}{8}$ .
1 mark
Complete $\frac{3}{7} = \frac{12}{?}$ .
1 mark
Write $\frac{10}{15}$ in simplest form.
2 marks
Write the shaded fraction in simplest form.
2 marks
Lee says $\frac{4}{6} = \frac{8}{9}$ . Is Lee correct? Explain without using a decimal.
2 marks
A garden has twenty equal plots. Eight grow beans. What fraction grows beans? Give a simplest-form answer.
2 marks

Read the worked solutions

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

Complete $\frac{1}{2} = \frac{?}{8}$ .
1 mark
The denominator is multiplied by four, so the numerator is also multiplied by four.
4
Complete $\frac{3}{7} = \frac{12}{?}$ .
1 mark
Three is multiplied by four. Seven times four is twenty-eight.
28
Write $\frac{10}{15}$ in simplest form.
2 marks
Both numbers have common factor five. Divide both by five.
$\frac{2}{3}$
Write the shaded fraction in simplest form.
2 marks
Six of sixteen parts are shaded: $\frac{6}{16}$ .
Divide both numbers by two.
$\frac{3}{8}$
Lee says $\frac{4}{6} = \frac{8}{9}$ . Is Lee correct? Explain without using a decimal.
2 marks
Doubling $\frac{4}{6}$ would give $\frac{8}{12}$ , not $\frac{8}{9}$ .
The numerator and denominator were not scaled by the same factor.
No.
A garden has twenty equal plots. Eight grow beans. What fraction grows beans? Give a simplest-form answer.
2 marks
The fraction is $\frac{8}{20}$ .
Divide both numbers by four to get two fifths.
$\frac{2}{5}$

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Curriculum reference & lesson scope

Australian Curriculum v9.0; SA Curriculum Mathematics 2026

Equivalence; mixed numbers; ordering; related-denominator addition/subtraction.

Official curriculum source ↗

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