Substitution means replacing the letter in an algebraic expression
with a given number, then calculating the result step by step.
The expression itself does not change — only the letter is swapped for the value.
✏️ Guided Example
Find the value of (9n + 7) ÷ 5 when n = 12.
STEP 1
Understanding the Problem
If n = 12, what is the value of 9n?
▶ 9n = 9 × n = 9 × 12 = 108
What is the value of 9n + 7?
▶ 108 + 7 = 115
What am I trying to find?
▶ The value of (9n + 7) ÷ 5 when n = 12.
Replace n
→
12
in the expression
(9n + 7) ÷ 5
STEP 2
Devising a Plan
▶ Draw a comparison model to show the structure of the expression.
STEP 3
Carrying Out the Plan
(9n + 7) ÷ 5
= (9 × 12 + 7) ÷ 5
= (108 + 7) ÷ 5
= 115 ÷ 5
= 23
= (9 × 12 + 7) ÷ 5
= (108 + 7) ÷ 5
= 115 ÷ 5
= 23
The value of (9n + 7) ÷ 5 when n = 12 is 23.
STEP 4
Looking Back
Check: (9 × n + 7) ÷ 5 = 23
9 × n + 7 = 23 × 5 = 115
9 × n = 115 − 7 = 108
n = 108 ÷ 9 = 12 ✓
9 × n + 7 = 23 × 5 = 115
9 × n = 115 − 7 = 108
n = 108 ÷ 9 = 12 ✓
💡 Key Idea: Replace the letter with the given number, then follow
BODMAS — work out brackets first, then division.
Always show each step clearly.
📝 Substitute the given value into the expression and work it out step by step.
Answer both parts, then click Lock In Answers.
1
Find the value of the algebraic expression 7r + 39 when r = 5.
(i) 1 mark
What is the value of 7r when r = 5?
(ii) 1 mark
What is the value of 7r + 39 when r = 5?
✅ Worked Answer
Substitute r = 5:
(i) 7r = 7 × 5 = 35
(ii) 7r + 39 = 35 + 39 = 74
(i) 7r = 7 × 5 = 35
(ii) 7r + 39 = 35 + 39 = 74
Value = 74
2
Find the value of the algebraic expression 12f − 20 when f = 13.
(i) 1 mark
What is the value of 12f when f = 13?
(ii) 1 mark
What is the value of 12f − 20 when f = 13?
✅ Worked Answer
Substitute f = 13:
(i) 12f = 12 × 13 = 156
(ii) 12f − 20 = 156 − 20 = 136
(i) 12f = 12 × 13 = 156
(ii) 12f − 20 = 156 − 20 = 136
Value = 136
3
Find the value of the algebraic expression (8p ÷ 3) + 5 when p = 9.
(i) 1 mark
What is the value of 8p ÷ 3 when p = 9?
(ii) 1 mark
What is the value of (8p ÷ 3) + 5 when p = 9?
✅ Worked Answer
Substitute p = 9:
(i) 8p ÷ 3 = (8 × 9) ÷ 3 = 72 ÷ 3 = 24
(ii) (8p ÷ 3) + 5 = 24 + 5 = 29
(i) 8p ÷ 3 = (8 × 9) ÷ 3 = 72 ÷ 3 = 24
(ii) (8p ÷ 3) + 5 = 24 + 5 = 29
Value = 29
4
Find the value of the algebraic expression 10 − (3x + 7) ÷ 5 when x = 6.
(i) 1 mark
What is the value of (3x + 7) ÷ 5 when x = 6?
(ii) 1 mark
What is the value of 10 − (3x + 7) ÷ 5 when x = 6?
✅ Worked Answer
Substitute x = 6:
(i) 3x + 7 = (3 × 6) + 7 = 18 + 7 = 25
(3x + 7) ÷ 5 = 25 ÷ 5 = 5
(ii) 10 − 5 = 5
(i) 3x + 7 = (3 × 6) + 7 = 18 + 7 = 25
(3x + 7) ÷ 5 = 25 ÷ 5 = 5
(ii) 10 − 5 = 5
Value = 5