Rearranging Formulae

Rearranging Formulae

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.

Example 1

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

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

A = πr2

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

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

Answer: r = √(frac(A)(π))

Example 2

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

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)

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