Substituting into formulas
Replace a variable with its value and carry units through the calculation.
Before you begin
- Powers and order of operations
- Reading algebraic expressions
Replace every occurrence consistently
To evaluate an expression, substitute the given number wherever its variable occurs. Use brackets around the substituted value, especially when a power or a negative value is involved. Then follow the order of operations. Evaluation finds a value for a chosen input; it does not ask you to solve for an unknown. Keep the original formula visible so that you can check each substitution.
Interpret the result and its units
A formula connects quantities. In A = lw, two lengths combine to produce area, so centimetres become square centimetres. Check that all lengths use compatible units before substitution. If a formula is defined only for positive lengths, an algebraically possible negative input is not a valid geometric measurement. A final value needs a unit and a sentence connecting it to the question.
Worked example
A cube has side length s = 1/2 m. Use V = s³ and A = 6s² to find its volume and surface area.
Show the worked solution
- For volume, substitute s = 1/2: V = (1/2)³ = 1/8.
- For surface area, first square the side: (1/2)² = 1/4; then 6 × 1/4 = 3/2.
- Volume uses cubic metres and surface area uses square metres.
V = 1/8 m³; A = 1.5 m².
Try it yourself
Evaluate 2a² + 1 when a = 3.
Common mistakes
- Evaluate powers before multiplying by a coefficient.
- Do not confuse perimeter units with area units.
What can you explain now?
Find the perimeter P = 2l + 2w for l = 3.5 cm and w = 2 cm.
Compare with the explanation
11 cm.
P = 2 × 3.5 + 2 × 2 = 7 + 4 = 11. Perimeter is a total length, so the unit remains centimetres.
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Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗