Equivalent fractions and mixed numbers | Year 7

01 / LEARN

The idea, step by step

Equal amounts, different parts

The denominator tells how many equal pieces make one whole. The numerator counts those pieces. If every piece is cut into the same number of smaller pieces, both numbers change but the amount stays the same.

Multiply or divide numerator and denominator by the same non-zero number to make an equivalent fraction. To simplify fully, divide by their greatest common factor. Use equal-sized wholes when comparing pictures.

Counting complete wholes

An improper fraction has a numerator at least as large as its denominator. Divide to find how many complete wholes it contains. The remainder counts the fractional part.

To convert a mixed number, multiply its whole part by the denominator, add the numerator, and keep the denominator. Check by reversing the conversion.

2 \frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{13}{5}

A common trap

Adding the same amount to top and bottom keeps a fraction unchanged.

Instead: Multiply both parts by the same non-zero number instead. For example, $\frac{1}{2} \neq \frac{2}{3}$ .

02 / WORKED EXAMPLES

See the thinking

Example 1

Simplify a fraction

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

18 and 24 share the greatest common factor 6.
$\frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4}$ .
3 and 4 share no factor greater than 1.

\frac{3}{4}

Example 2

Find complete wholes

Write $\frac{17}{5}$ as a mixed number.

17 divided by 5 is 3 remainder 2.
Three complete wholes and two fifths give $3 \frac{2}{5}$ .
Check: $3 \times 5 + 2 = 17$ .

3 \frac{2}{5}

Check your understanding

Which equals $\frac{3}{5}$ : $\frac{6}{10}$ or $\frac{6}{8}$ ?

Show answer

$\frac{6}{10}$

Both parts of three fifths have been multiplied by 2.

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Simplify $\frac{15}{20}$ .
2 marks
Complete $\frac{4}{7} = \frac{□}{28}$ .
2 marks
Write $2 \frac{3}{5}$ as an improper fraction.
2 marks
Write $\frac{23}{6}$ as a mixed number.
2 marks
Explain why $\frac{6}{8}$ is not in simplest form.
2 marks
One board is $1 \frac{1}{2}$ m long. Another is $\frac{6}{4}$ m. Are their lengths equal?
3 marks

Read the worked solutions

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

Simplify $\frac{15}{20}$ .
2 marks
Divide numerator and denominator by 5.
$\frac{3}{4}$
Complete $\frac{4}{7} = \frac{□}{28}$ .
2 marks
28 is 7 times 4, so the numerator must also be multiplied by 4.
16
Write $2 \frac{3}{5}$ as an improper fraction.
2 marks
$2 \times 5 + 3 = 13$ ; keep denominator 5.
$\frac{13}{5}$
Write $\frac{23}{6}$ as a mixed number.
2 marks
23 divided by 6 is 3 remainder 5.
$3 \frac{5}{6}$
Explain why $\frac{6}{8}$ is not in simplest form.
2 marks
6 and 8 share the factor 2.
$\frac{6}{8} = \frac{3}{4}$
One board is $1 \frac{1}{2}$ m long. Another is $\frac{6}{4}$ m. Are their lengths equal?
3 marks
$1 \frac{1}{2} = \frac{3}{2} = \frac{6}{4}$ .
Both amounts use metres.
Yes.

Checking saved progress…

Continue learning

Ordering rational numbers on number lines

Next lesson

Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Equivalent fractions and mixed numbers; ordering rational numbers on number lines; adding/subtracting fractions; multiplying/dividing fractions; four operations with decimals; converting between fractions and decimals; multi-step problems and checking estimates.

Official curriculum source ↗

Back to Fractions and decimals