Substitution
Replacing letters with numbers in a formula and calculating the result.
What is Substitution?
Substitution means replacing letters (variables) in a formula or expression with given number values, then calculating the result. It is one of the most straightforward algebra skills but requires careful attention to BIDMAS.
In the 11+ exam, substitution questions may ask you to evaluate an expression, use a formula (like area or perimeter), or find the value of one variable given the others.
Step-by-Step Method
Write out the expression or formula
Copy it clearly, leaving space to substitute.
Replace each letter with its given value
Use brackets around the substituted numbers to keep things clear: 2a becomes 2(3).
Apply BIDMAS to calculate
Remember the order of operations: brackets, indices, division/multiplication, addition/subtraction.
Work through one step at a time
Do not try to do everything in your head – show each step.
Check your answer makes sense
If the formula is for perimeter, is your answer a reasonable length? Common sense checks catch errors.
Worked Examples
If a = 3 and b = 5, find 2a + b.
Working
- Replace a with 3 and b with 5: 2(3) + 5.
- 2 x 3 = 6.
- 6 + 5 = 11.
If x = 4, find x squared – 3x + 2.
Working
- Replace x with 4: (4) squared – 3(4) + 2.
- 16 – 12 + 2.
- 16 – 12 = 4.
- 4 + 2 = 6.
Find the perimeter using P = 2(l + w) when l = 8 and w = 5.
Working
- Replace l with 8 and w with 5: P = 2(8 + 5).
- Brackets first: 8 + 5 = 13.
- Then multiply: 2 x 13 = 26.
Common Mistakes
Forgetting that 2a means 2 x a, not 2 and a side by side.
In algebra, a number next to a letter always means multiply: 3b = 3 x b.
Not using BIDMAS after substituting, calculating left to right instead.
After substituting, treat the result as a normal calculation and follow BIDMAS.
Sign errors when substituting negative numbers.
Use brackets around negative numbers: if x = -2, then x squared = (-2) squared = 4, not -4.
Top Tips
- Always use brackets when substituting to avoid errors: write 2(3) not 23.
- Remember that x squared means x times x, not x times 2.
- If a formula has multiple variables, replace them one at a time.
- Check your arithmetic carefully – substitution itself is easy, but calculation errors are common.
Ready to practise?
Put these techniques into action with our free practice papers.
Practise Maths Questions