Changing the subject

Changing the subject means rearranging a formula so a different letter is on its own. Do the same to both sides, undoing operations in the reverse order to how they were done to the letter.

Key facts

  • Undo + with −, × with ÷, squaring with square rooting.
  • Undo in reverse order (last done, first undone).
  • If the new subject appears twice, collect those terms and factorise.

Worked examples

Example 1

Make r the subject of A = πr².

  1. r was squared, then multiplied by π.
  2. Divide by π. A/π = r²
  3. Square root. r = √(A/π)

Answer: r = √(A/π)

Example 2

Make x the subject of ax + b = cx + d.

  1. Get the x terms together. ax − cx = d − b
  2. Factorise. x(a − c) = d − b
  3. Divide. x = (d − b)/(a − c)

Answer: x = (d − b)/(a − c)