Rearranging Formulae

Things to remember:

• Don’t rush it. You must go through each stage of your method and not try to skip any.

• If you are making x the subject it means that you want to end up with x= and this is the only x in your answer.

• Whatever you do to one side of the equals sign you must do to the other.

Example

Rearrange the formula a = x + .to make x the subject.

dcx

Method -

multiply both sides by d

rearrange to get x’s on the left

factorise

divide by (d + c)

a = x + dcx

ad = dx + cx

dx + cx = ad

x(d + c) = ad

cdad

x =

Example

Rearrange the formula a = + .to make p the subject.

q1

Method -

multiply both sides by pq

rearrange to get p’s on the left

factorise

divide by (aq – 1)

a = + q1

apq = q + p

apq – p = q

p(aq – 1) = q

1aqq

p =

p1

p1

Example

Rearrange the formula a = b + .to make p the subject.

pc1

Method -

multiply both sides by 1 + p

expand brackets

rearrange to get p’s on the left

divide by (a – b)

a = b + pc1

a(1 + p) = b(1 + p) + c

a + ap = b + bp + c

ap – bp = b + c – a

baacb

p =

p(a – b) = b + c – a factorise

Example

Rearrange the formula s = b + .to make t the subject.

Method -

subtract b from both sides

square both sides

rearrange to get t on the left

multiply by p

s = b +

s – b =

(s – b)² =

= (s – b)²

t = p(s – b)²

pt

pt

pt

pt

pt