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 +
make x the subject.
Method -
a=x+
cx
d
.to
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
factorise
x=
ad
dc
divide by (d + c)
Example
Rearrange the formula a =
make p the subject.
Method -
a=
1
p
+
1
q
.to
1
1
+ q
apq = q + p
multiply both sides by pq
apq – p = q
rearrange to get p’s on the left
p(aq – 1) = q
factorise
p
q
p = aq  1
divide by (aq – 1)
Example
c
Rearrange the formula a = b + 1  p .to
make p the subject.
c
Method - a = b +
1 p
a(1 + p) = b(1 + p) + c
a + ap = b + bp + c
multiply both sides by 1 + p
expand brackets
ap – bp = b + c – a
rearrange to get p’s on the left
p(a – b) = b + c – a
factorise
p=
bca
ab
divide by (a – b)
Example
Rearrange the formula s = b +
make t the subject.
Method -
s=b+
s–b=
(s – b)² =
t
p
t
p
.to
t
p
t
p
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