YEAR 7 · LINEAR EQUATIONS · 15 MIN

One-step multiplication/division equations

Use division to undo multiplication and multiplication to undo division, recognising that a coefficient means multiplication.

In this lesson

Interpret a coefficient such as 4 in 4x
Solve one-step multiplication/division equations
Check a multiplicative equation

Before you start

Multiplication and division facts
Equality and balancing

01 / LEARN

Understand the idea.

Undo a multiplication

A number directly beside a variable means multiplication: $4 x$ means $4 \times x$ . In $4 x = 28$ , four equal groups total $28$ , so divide both sides by $4$ to find one group.

The multiplying number is the coefficient. Undo multiplication by dividing by the entire coefficient. For $12 n = 60$ , use division by $12$ , giving $n = 5$ ; subtraction would not undo the multiplication.

Undo a division

A fraction bar means division. Thus $\frac{y}{5} = 8$ says that one of five equal groups contains $8$ . Multiply both sides by $5$ to recover the whole amount, giving $y = 40$ .

Choose the inverse of the operation on the variable, not an operation suggested by where a number is printed. Check a multiplication equation by multiplying your solution, and check a division equation by dividing it in the original expression.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Find one equal group

Solve $7 a = 56$ .

Worked solution

1
Divide both sides by 7.
$\frac{7 a}{7} = \frac{56}{7}$
The coefficient 7 multiplies a, so division by 7 recovers one group.
2
Simplify.
$a = 8$
Seven equal groups of 8 have total 56.
3
Check the original product.
$7 \times 8 = 56$
The substituted value gives the required total.

Answer

$a = 8$

EXAMPLE 02

Recover the full collection

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

Worked solution

1
Multiply both sides by 6.
$6 \times \frac{m}{6} = 6 \times 9$
Multiplication by 6 undoes division by 6.
2
Calculate the original amount.
$m = 54$
Six groups of 9 make the whole amount.
3
Check the original quotient.
$\frac{54}{6} = 9$
The proposed value divided by 6 equals the given right side.

Answer

$m = 54$

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

$q = 48$ .

Multiply both sides of $\frac{q}{8} = 6$ by $8$ to obtain $q = 48$ . Dividing $48$ by $8$ gives $6$ , as required.

Keep practising

6 worksheet questions · 13 marks

Open worksheet 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.

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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 ↗

In this lesson

Understand the idea.

Undo a multiplication

Undo a division

See the method in action.

Find one equal group

Divide both sides by 7.

Simplify.

Check the original product.

Recover the full collection

Multiply both sides by 6.

Calculate the original amount.

Check the original quotient.

Try it yourself.

Check your understanding

Keep practising