Equivalent fractions | Year 5

01 / LEARN

Understand the idea.

Different names, same share

Equivalent fractions name the same share of a whole using different-sized pieces. Cutting every third in half changes thirds into sixths: the same shaded two thirds becomes four sixths. More selected pieces are needed because each new piece is smaller.

Keep the reference whole the same size when comparing pictures. Two fractions can show the same share but different actual amounts if one whole is larger. Within one model, all pieces counted by a denominator must also be equal.

Scale both numbers together

To make an equivalent fraction, multiply both numerator and denominator by the same positive whole number. The numerator counts selected pieces and the denominator counts pieces per whole, so changing both together preserves the share.

To simplify, divide both numbers by a common factor. For $\frac{8}{12}$ , dividing both by $4$ gives $\frac{2}{3}$ . Stop when no factor greater than one divides both numbers; multiplying back should recover the original fraction.

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

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Make sixths into eighteenths

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

Worked solution

1
Find how the denominator changes.
$18 \div 6 = 3$
Each sixth must be split into three equal pieces to make eighteenths.
2
Apply the same scale factor to the numerator.
$5 \times 3 = 15$
The five selected sixths each become three selected eighteenths.
3
Write the equivalent fraction.
$\frac{5}{6} = \frac{15}{18}$
Both numerator and denominator have been multiplied by 3, preserving the share.

Answer

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

EXAMPLE 02

Simplify a set of counters

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

Worked solution

1
Write the selected part over the total.
$\frac{12}{18}$
12 counters are blue out of 18 counters altogether.
2
Find a factor common to both numbers.
$12 = 6 \times 2, 18 = 6 \times 3$
Grouping in sixes divides both counts by $6$ , giving $2$ blue groups out of $3$ groups altogether without changing the blue share.
3
Divide both numbers by six.
$\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}$
2 and 3 have no common factor greater than 1, so two thirds is simplest form.

Answer

$\frac{12}{18} = \frac{2}{3}$ of the counters are blue.

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

Yes.

Yes: multiplying both numerator and denominator of $\frac{3}{4}$ by $3$ gives $\frac{9}{12}$ . The numerator and denominator change by the same factor, so the share stays equal.

Keep practising

6 worksheet questions · 10 marks

Open worksheet 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 ↗

In this lesson

Understand the idea.

Different names, same share

Scale both numbers together

See the method in action.

Make sixths into eighteenths

Find how the denominator changes.

Apply the same scale factor to the numerator.

Write the equivalent fraction.

Simplify a set of counters

Write the selected part over the total.

Find a factor common to both numbers.

Divide both numbers by six.

Try it yourself.

Check your understanding

Keep practising