One-step multiplication/division equations | Year 7

01 / LEARN

The idea, step by step

Undo a multiplication

The expression $4 x$ means $4 \times x$ . In $4 x = 28$ , four equal groups have a total of 28. Divide both sides by 4 to find one group: $x = 7$ .

The coefficient is the number multiplying the variable. Divide by that whole coefficient, not by one digit chosen from it. For example, $12 n = 60$ is undone by dividing both sides by 12.

Undo a division

In $y \div 5 = 8$ , the unknown has been split into five equal groups. Each group contains 8. Multiply both sides by 5 to recover the original total: $y = 40$ .

A fraction bar also means division: $\frac{y}{5} = 8$ is the same equation. Keep the numerator, denominator and equals sign clear. Check by dividing your final value by 5 to see whether the original equation is true.

A common trap

For $5 x = 35$ , subtract 5 because 5 is next to x.

Instead: $5 x$ means multiplication, so use division: $x = 35 \div 5 = 7$ . Subtracting 5 would undo a different operation.

02 / WORKED EXAMPLES

See the thinking

Example 1

Find one equal group

Solve $7 a = 56$ .

The variable is multiplied by 7.
Divide both sides by 7: $a = 56 \div 7$ .
$a = 8$ .
Check: $7 \times 8 = 56$ .

a = 8

Example 2

Recover the full collection

Solve $\frac{m}{6} = 9$ .

The variable has been divided by 6.
Multiply both sides by 6: $m = 9 \times 6$ .
$m = 54$ .
Check: $54 \div 6 = 9$ .

m = 54

Check your understanding

Solve $\frac{q}{8} = 6$ .

Show answer

$q = 48$ .

Multiply both sides by 8: $q = 6 \times 8 = 48$ . Check: $48 \div 8 = 6$ .

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Solve $3 x = 27$ .
2 marks
Solve $8 n = 48$ .
2 marks
Solve $12 a = 84$ .
2 marks
Solve $\frac{p}{5} = 11$ .
2 marks
Solve $y \div 9 = 4$ .
2 marks
Six identical packs contain 42 cards in total. Let $c$ be the number of cards in each pack. Write and solve an equation.
3 marks

Read the worked solutions

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

Solve $3 x = 27$ .
2 marks
Divide both sides by 3.
$x = 27 \div 3 = 9$ .
Check: $3 \times 9 = 27$ .
$x = 9$
Solve $8 n = 48$ .
2 marks
Divide both sides by 8.
$n = 48 \div 8 = 6$ .
Check: $8 \times 6 = 48$ .
$n = 6$
Solve $12 a = 84$ .
2 marks
Divide both sides by 12.
$a = 84 \div 12 = 7$ .
Check: $12 \times 7 = 84$ .
$a = 7$
Solve $\frac{p}{5} = 11$ .
2 marks
Multiply both sides by 5.
$p = 11 \times 5 = 55$ .
Check: $55 \div 5 = 11$ .
$p = 55$
Solve $y \div 9 = 4$ .
2 marks
Multiply both sides by 9.
$y = 4 \times 9 = 36$ .
Check: $36 \div 9 = 4$ .
$y = 36$
Six identical packs contain 42 cards in total. Let $c$ be the number of cards in each pack. Write and solve an equation.
3 marks
Six equal pack amounts give $6 c = 42$ .
Divide both sides by 6: $c = 7$ .
Check: $6 \times 7 = 42$ .
$6 c = 42$ ; $c = 7$ cards per pack.

Checking saved progress…

Continue learning

Straightforward two-step equations

Next lesson

Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Year 7 linear equations with natural-number solutions: equality, inverse operations, substitution checks and familiar models. Formal variables-on-both-sides techniques are not required here.

Official curriculum source ↗

Back to Linear equations