Rearrange simple formulae

Objective. Change the subject of a one- or two-step formula.

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Learn: the key idea

Rearranging a formula means changing which letter is the subject by performing the same inverse operation to both sides, isolating the desired letter step by step. To make x the subject of y = 3x + 2, first subtract 2 from both sides to get y − 2 = 3x, then divide both sides by 3 to get x = (y − 2) ÷ 3. Each step must undo the operation applied to the subject in reverse order to how it was built up, treating the formula exactly like an equation that must stay balanced throughout.

Worked example

Rearrange the formula p = 4q − 7 to make q the subject through formula rearrangement.

1 $Add 7 to both sides to isolate the term with q: p + 7 = 4q$
2 $Divide both sides by 4: (p + 7) \div 4 = q$
3 $Write q as the subject: q = (p + 7) \div 4$
4 $Check by substituting back: if q = (p+7)/4, then 4q - 7 = p + 7 - 7 = p$

Answer: q = (p + 7) ÷ 4

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Common mistake. Pupils often divide only one term by the coefficient when rearranging, turning y = 3x + 2 into x = y ÷ 3 + 2 instead of correctly subtracting 2 first and then dividing the whole expression by 3.

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