Rearranging Formulae

Rearranging Formulae

GCSE(F) GCSE(H)

A formula is normally arranged such that one variable (letter) is on one side of the equals sign with all the other variables and numbers on the other side of the equals sign. The letter on its own is called the subject of the formula.

Sometimes it is necessary to change the subject of a formula. This is known as rearranging a formula.

The volume of a triangular prism is given by V = `frac(1)(2)`bhl, where V is the volume, b is the width of the base, h is the vertical height and l i the length of the prism. To make l the subject of the formula, it is necessary to rearrange it:

V = `frac(1)(2)`bhl

2V = bhl (multiply both sides by 2 to cancel the `frac(1)(2)` on the right hand side)

`frac(2V)(b)` = hl (divide both sides by b)

`frac(2V)(bh)` = l (divide both sides by h

As l is now on its own on one side of the formula, it has become the subject of the formula.

Examples

1. Using the formula for the area of a circle, make the radius the subject of the formula.

Answer: r = √(`frac(A)(π)`)

The formula for the area of a circle is A = πr2. Rearrange:

A = πr2

`frac(A)(π)` = r2(divide both sides by π)

`frac(A)(π)` = r (square root both sides).

2. Rearrange the formula p = 5a - `frac(1)(b)` to give a in terms of b and p.

Answer: a = `frac(1)(5)`(p + `frac(1)(b)`)

p = 5a - `frac(1)(b)`

p + `frac(1)(b)` = 5a (add `frac(1)(b)` to both sides)

`frac(1)(5)`(p + `frac(1)(b)`) = a (divide both sides by 5)