Changing the Subject of a Formula
Changing the subject of a formula means rearranging an equation so that a different letter is isolated on one side, using the same inverse operations as solving an equation. It is a core GCSE algebra skill used whenever a formula, such as speed = distance / time, needs to be rewritten to make a different variable the subject.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify the letter that needs to become the new subject and treat every other letter as if it were a number.
- Undo the operations applied to the subject in reverse order (the opposite of BIDMAS), using inverse operations: addition undoes subtraction, multiplication undoes division, and so on.
- If the subject appears inside a bracket, first undo anything outside the bracket, then expand or divide to release it.
- If the subject appears more than once, expand any brackets, collect all terms containing the subject on one side, then factorise it out before dividing.
- If the formula involves a square or square root, square or square-root both sides as the very last step, once the subject's term is isolated.
- Check your rearranged formula by substituting numbers into both the original and new versions to confirm they give the same result.
Worked example
Make x the subject of the formula y = 5x - 7.
- Add 7 to both sides to isolate the term in x: y + 7 = 5x.
- Divide both sides by 5: (y + 7) / 5 = x.
- Rewrite with x as the subject: x = (y + 7) / 5.
- State the final answer: x = (y + 7) / 5.
Practice questions
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Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
Make x the subject of the formula y = 7x + 2.
The formula for the volume of a cylinder is V = pi x r^2 x h. (a) Make h the subject of the formula. (2) (b) Find h when V = 400, r = 5 and pi = 3.14, giving your answer correct to 1 decimal place. (2)
Make x the subject of the formula: y = (4x + 3)/(x - 2)
Free printable worksheet
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