Simple substitution
Algebraic substitution is like solving a puzzle — you replace letters with numbers to find the answer. It's a key skill in real-world problem-solving, from calculating mobile phone bills to working out travel times, and it forms the foundation for more advanced algebra later on. Jump to the questions
Practise now
Substitute the given values and calculate the result.
Topic guide
What this worksheet practises
This worksheet provides practice on algebraic substitution, where you replace letters in an expression with specific numerical values. It tests your understanding of invisible algebraic rules (like hidden multiplication) and the Order of Operations (BIDMAS).
Key method
The safest way to substitute is to use brackets for every number you insert.
- Look at the algebraic expression (e.g. 3a + b).
- Replace every letter with its given number, putting that number entirely inside brackets (e.g. if a=4 and b=5, write 3(4) + (5)).
- Expand any hidden maths. A number touching a bracket means multiply (3(4) means 3 × 4). Letters touching each other (xy) means multiply. A fraction line means divide.
- Calculate the final answer, strictly following BIDMAS (Indices first, then Multiplication/Division, then Addition/Subtraction).
Worked example
Find the value of 5x² − 2y when x = 3 and y = 4.
Step 1: Substitute the numbers into the expression using brackets.
5(3)² − 2(4)
Step 2: Follow BIDMAS. We must do the Indices (squaring) first.
The (3)² becomes 9.
The sum is now: 5(9) − 2(4)
Step 3: Do the multiplication.
5 × 9 = 45.
2 × 4 = 8.
The sum is now: 45 − 8
Step 4: Do the final subtraction.
45 − 8 = 37.
The final answer is 37.
Common mistakes to avoid
The most catastrophic mistake happens with expressions like 5x². A student substituting x=3 might calculate 5 × 3 = 15, and then square the 15 to get 225. This violates BIDMAS. You must square the 'x' first, and then multiply the result by 5. The correct answer is 45.
Things to remember
When substituting negative numbers, brackets are essential. If you substitute x = −3 into the expression x², writing −3² on a calculator will give you −9 (which is wrong). Writing it with brackets as (−3)² gives the correct answer of +9.