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

cx

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

Method a = x +

cx d

ad = dx + cx multiply both sides by d dx + cx = ad rearrange to get x’s on the left x(d + c) = ad x =

d ad  c

factorise divide by (d + c)

Example

make p the subject.

1 p 1

Method -

1

a = +

1 q

apq = q + p apq – p = q p(aq – 1) = q p =

aq q  1

multiply both sides by pq rearrange to get p’s on the left factorise divide by (aq – 1)

Example

c

Rearrange the formula a = b + .to

1

make p the subject.

Method a = b +

1 c  p

a(1 + p) = b(1 + p) + c multiply both sides by 1 + p a + ap = b + bp + c ap – bp = b + c – a p(a – b) = b + c – a p =

b  a c   b a

expand brackets rearrange to get p’s on the left factorise divide by (a – b)

Example

make t the subject.

Method s = b +

t p

s – b = (s – b)² =

t p p t t p

= (s – b)² t = p(s – b)² subtract b from both sides square both sides rearrange to get t on the left multiply by p