1. What is Rearranging Formulae?
The ability to rearrange formulas or rewrite them in different ways is an important skill in algebra.
You will be familiar with the formula for the area of a rectangle which states A = l × w. Here A is the area, l is the length and w is the width. In the form A = l × w, we say that A is the subject of the formula. Usually, the subject of a formula is on its own on the left-hand side. If you know the value of l and w then you can substitute directly to find A.
2. Changing the Subject of the Formula
Changing the subject changes the form of the equation to display it in a different way. This is sometimes called the rearranging formula.
To rearrange a formula you may
- add or subtract the same term to or from both sides
- multiply or divide both sides by the same term
2.1 Simple Formula
Example: Make 𝑥 the subject of the formula of a + 3x = y - b
a + 3x = y - b
Subtract a from both sides
3x = y - b - a
Divide both sides by 3
2.2 Formulae with brackets and fractions
If there are brackets included in the formula then it is easier if you expand them first. Remove any fractions by multiplying by the denominator/s
Example: Make 𝑥 the subject of the formula of a(x + y) = 2ay
Solution:
Example:
2.3 Formulae which require factorising first
When changing the subject you start by collecting the term that you want on one side of the equation. In some cases, the required subject will appear more than once in the given formula. In these examples, we factorise the terms involving the subject before proceeding further.
Example:
2.4 Formulae with roots and powers
If a formula contains a power or a root then this must be isolated before performing the inverse operation. It is important to remember that square and square root are inverse functions, similarly, cube and cube root.
Example:
