Change the subject of a formula

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Change the subject of a formula

Rearranging keeps an equation equivalent while isolating a chosen variable. Apply the same valid operation to both sides. Reverse the operations surrounding the variable, using brackets to preserve any grouped numerator.

In P=2l+2w, subtract 2w from each side, then divide the entire remaining expression by 2. The result l=(P−2w)/2 is not P−w. Where division introduces a variable denominator, state that it cannot be zero.

The rearranged formula should reproduce the original relationship when substituted back. It may also be checked with a simple numerical example. If the chosen variable appears more than once, collecting its terms and factorising can be necessary before division.

Worked example: Make l the subject of P=2l+2w.

Subtract 2w: P−2w=2l.

Divide both sides by 2, keeping the numerator grouped.

Answer: l=(P−2w)/2.

Check your understanding: Make t the subject of d=vt when v≠0.

Answer: t=d/v.

Why: Division by the nonzero v reverses multiplication; v=0 would not determine a unique t from this division.