Solving One-Step Equations • Topic 2 of 3

Solving Multiplication & Division Equations

Multiplication Equations:

To solve 3z = 18, divide both sides by 3.

3z = 18
3z ÷ 3 = 18 ÷ 3
z = 6

Division Equations:

To solve m/2 = 7, multiply both sides by 2.

m/2 = 7
m/2 × 2 = 7 × 2
m = 14
MULTIPLICATION EQUATION: 3z = 18

    3z = 18 means 3 groups of z equal 18
    
    ┌─────────────────────────────────┐
    │  ┌─┐┌─┐┌─┐                     │
    │  │z││z││z│     18              │
    │  └─┘└─┘└─┘                     │
    │  ════════════════════         │
    │                                 │
    │  Divide both sides by 3:        │
    │                                 │
    │  ┌─┐                           │
    │  │z│          6                │
    │  └─┘                           │
    │  ════════════════════         │
    └─────────────────────────────────┘


DIVISION EQUATION: m/2 = 7

    m/2 = 7 means half of m equals 7
    
    ┌─────────────────────────────────┐
    │                                 │
    │     m                           │
    │   ┌─┐                           │
    │   │ │  half = 7                 │
    │   │ │                           │
    │   └─┘                           │
    │   ════════════════════         │
    │                                 │
    │  Multiply both sides by 2:      │
    │                                 │
    │     m = 14                      │
    │   ┌───┐                         │
    │   │   │                         │
    │   │   │                         │
    │   └───┘                         │
    │   ════════════════════         │
    └─────────────────────────────────┘
Solved Examples
1
Worked Example

Solve: 3z = 18

Solution
  • Divide both sides by 3
  • 3z ÷ 3 = 18 ÷ 3
  • z = 6
  • Answer: z = 6
2
Worked Example

Solve: m/2 = 7

Solution
  • Multiply both sides by 2
  • (m/2) × 2 = 7 × 2
  • m = 14
  • Answer: m = 14
3
Worked Example

Solve: 5a = 35

Solution
  • Divide both sides by 5
  • 5a ÷ 5 = 35 ÷ 5
  • a = 7
  • Answer: a = 7
4
Worked Example

Solve: n/6 = 9

Solution
  • Multiply both sides by 6
  • (n/6) × 6 = 9 × 6
  • n = 54
  • Answer: n = 54

Key Points

  • Multiplication → divide both sides
  • Division → multiply both sides
  • Think: "Do the opposite operation"
  • Always check your answer
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.To solve $3x=12$, you:
Explanation: Divide by $3$.
Q2.To solve $\tfrac{x}{4}=5$, you:
Explanation: Multiply by $4$.
Q3.The solution of $5x=20$ is:
Explanation: $x=4$.
Q4.Multiplication and division are ___ operations.
Explanation: Inverse.
Practice more MCQs → 📝 Assignment · 35 marks