Transcript Rearranging Formulae - St. Brendan's Sixth Form College

Rearranging Equations
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.
Rearrange the equation to make a the subject
This means
we want to
rearrange
the
equation so
it says
a=
b = 5a + 21
-21
-21
÷5
÷5
b – 21 = 5a
b – 21 = a
5
Our answer should say ... a = b – 21
5
Rearrange the equation to make t the subject
This means
we want to
rearrange
the
equation so
it says
t=
h = 13 + 7t
-13
-13
÷7
÷7
h – 13 = 7t
h – 13 = t
7
Our answer should say ... t = h – 13
7
Exercise One
Rearrange each equation to make s the subject
1. u = 11s + 3
2. w = 8s + p
3. q = 3s + 4t
4. 7s + m + t = l
5. a = 3(s + 4) Hint: You need to expand the
brackets first
6. 4 = g(s – 7)
7. 22 + 5s = g
8. r = q – 3s
Rearrange each equation to make s the subject
1. u = 11s + 3

2. w = 8s + p

3. q = 3s + 4t

4. 7s + m + t = l 
5. a = 3(s + 4)

6. 4 = g(s – 7)

7. 22 + 5s = g

8. r = q – 3s

s=u-3
11
s=w–p
8
s = q – 4t
3
s=l–m–t
7
s = a – 12 = a - 4
3
3
s = 4 + 7g = 4 + 7
g
g
s = g - 22
5
s=q-r
3
Rearrange the equation to make v the subject
This means
we want to
rearrange
the
equation so
it says
v=
e = 3v + t
x5
5
x5
5e = 3v + t
-t
-t
5e – t = 3v
÷3
÷3
5e – t = v
3
Our answer should say ... v = 5e – t
3
Rearrange the equation to make p the subject
This means
we want to
rearrange
the
equation so
it says
p=
m=p+n
-n
2
-n
m-n=p
x2
2
x2
2(m – n) = p
Our answer should say ... p = 2(m – n)
Example
more difficult
cx
Rearrange the equation a = x +
d
to make x the subject.
Method -
cx
a=x+
d
ad = dx + cx
multiply both sides by d
dx + cx = ad
rearrange to get x’s on the left
x(d + c) = ad
ad
x=
dc
factorise
divide by (d + c)
Example
more difficult
1 1
Rearrange the equation a = +
p q
to make p the subject.
Method -
1 1
a= + q
p
apq = q + p
multiply both sides by pq
apq – p = q
rearrange to get p’s on the left
p(aq – 1) = q
q
p = aq  1
factorise
divide by (aq – 1)
Example
more difficult
Rearrange the equation a = b +
to make p the subject.
c
Method - a = b +
1 p
a(1 + p) = b(1 + p) + c
a + ap = b + bp + c
c
1 p
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
bca
p=
a b
factorise
divide by (a – b)
Example
more difficult
Rearrange the equation s = b +
to make t the subject.
Method -
s=b+
s–b=
(s – b)² =
t
p
t
p
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
Test Yourself
Check your
answers on
previous
slides
1. Rearrange the equation a = x + cx
d
to make x the subject.
2. Rearrange the equation a = 1 + 1
p
q
to make p the subject.
3. Rearrange the equation a = b + c
1 p
to make p the subject.
4. Rearrange the equation s = b + t
p
to make t the subject.