Rearranging Formulae definition
Rearranging formulae means changing a formula so that a different letter becomes the subject. The subject of a formula is the letter that is on its own on one side of the equals sign. For example, in the formula speed equals distance divided by time, speed is the subject. If we rearrange the formula to make distance the subject, we get distance equals speed times time.
Rearranging formulae uses the same balance idea as solving equations. Whatever operation is done to one side must also be done to the other side. The aim is to isolate the required variable. For example, if A equals l times w and you want w, divide both sides by l. This gives w equals A divided by l. The value of the formula has not changed; only the subject has changed.
Rearranging formulae is used in algebra, geometry, graphs, science, mechanics, physics, chemistry, finance and real-life modelling. At GCSE level, students rearrange simple and more complex formulas involving multiplication, division, addition, subtraction, powers, roots and brackets. At A-Level, rearranging is needed in functions, calculus, vectors, logarithms, exponentials and mechanics problems.
Inverse operations are the key to rearranging. Addition is undone by subtraction, subtraction is undone by addition, multiplication is undone by division, and division is undone by multiplication. If y equals 3x plus 5 and you want x, first subtract 5 from both sides to get y minus 5 equals 3x. Then divide by 3 to get x equals y minus 5 all divided by 3.
Fractions in formulae need careful handling. If s equals d divided by t and you want d, multiply both sides by t to remove the denominator. This gives st equals d, so d equals st. If you want t, start from s equals d divided by t, multiply by t to get st equals d, and then divide by s to get t equals d divided by s. Each step keeps the equation balanced.
Brackets are another common feature. If P equals 2l plus 2w and you want l, first subtract 2w from both sides to get P minus 2w equals 2l. Then divide by 2 to get l equals P minus 2w all divided by 2. Students should use brackets mentally or in writing when dividing a whole expression, so that every term is treated correctly.
Rearranging formulae is useful because one formula can answer different questions. In science, a formula might be given for speed, but the question may ask for time. In geometry, a formula might give area, but the question may ask for height. Rearranging allows students to use the same relationship flexibly instead of memorising many separate versions.
Related ideas include formula, equation, subject, variable, inverse operations, substitution, solving equations, brackets and algebraic fractions. A clear definition of rearranging formulae helps students understand that the goal is to make one letter stand alone. In exams, identify the target subject first, undo operations in a logical order and check by substituting simple values if possible.