Rearranging Formulas

  • Rearranging formulas involves changing the subject of the formula. This requires an understanding of basic algebraic operations such as addition, subtraction, multiplication, and division, and how to ‘undo’ these operations.

  • The basic principle of rearranging formulas is to isolate the variable we want to solve for, by performing the same operation on both sides of the equation.

  • Adding or subtracting: If a variable you wish to isolate has other terms added or subtracted to it, you can isolate it by subtracting or adding the same value from both sides.

  • For example, if the formula is ‘a = b + c’, and you want to make ‘b’ the subject, you would subtract ‘c’ from both sides to get ‘a - c = b’.

  • Multiplying or dividing: If a term involving the variable you want to isolate is being multiplied or divided, you can isolate it by dividing or multiplying both sides by the same value.

  • For example, if ‘a = bc’, and you want ‘b’ to be the subject, you would divide both sides by ‘c’, to get ‘a/c = b’.

  • When dealing with expressions in brackets, your first step should generally be to expand the brackets.

  • Powers and roots: If the variable is raised to a power, you can use roots to isolate it. Conversely, if the variable is under a root, you can use powers to isolate it.

  • For example, if ‘a = b²’, and you want to make ‘b’ the subject, you would take the square root of both sides to get √a = b.

  • In the case of formulas with ‘fractions’, we try to ‘clear’ the fractions by multiplying throughout by the denominator.

  • Keep in mind the ‘order of operations’ (also known as BIDMAS/BODMAS/PEDMAS) when both sides are complicated – brackets, indices, division and multiplication (from left to right), addition and subtraction (from left to right).

  • Always double-check the final rearranged formula by substituting values and seeing if both sides of the equation are equal.

  • It’s crucial to get comfortable with all these procedures, so enough practice is essential to mastering rearranging formulas in algebra.