Gcse Maths - Changing the subject of a method
Rearranging Formulae
Gcse Maths - Changing the subject of a method
Why rearrange formulae?
The formula d = st expresses distance (d), in terms of speed (s) and time (t).
It is sometimes indispensable to write a formula in a different, but equivalent form.
e.g. S = d/t
What is the 'subject' of a formula?
In formulae, a particular changeable appears on the Lhs of the equation.
This is called the subject of the formula.
In the formula d = st , d is the subject of the formula,
whereas in s = d/t, s is the subject of the formula.
The process of expressing (s) in terms of (d) and (t) is known as
rearranging or changing the subject of the formula.
Example 1
Make n the subject of the formula:
m = 3 n + 5
Method
Subtract 5 from both sides.
m - 5 = 3 n
Divide both sides by 3:
1/3 ( m - 5 ) = n
Rearrange so that subject is on Lhs:
Solution
n = 1/3 ( m - 5 )
Exercise
1. Make t the subject of the formula:
(i) y = 3 t + 5x
.........................................................
.........................................................
t =.................................
(ii) v = 3 x - 4 tz
.........................................................
.........................................................
t =.................................
(iii) s = (t/p) - 2r
.........................................................
.........................................................
t =.................................
Solutions
1. (i) t = (1/3) (y - 5x )
(ii) t = (3x - v) / 4z
(iii) t = p (s + 2r )
Required subject Occurs more than Once
If the required subject appears more than once in the primary formula,
we need first to secure the terms with the new subject and then factorise.
Example
Make p the subject of the formula:
r = 3 p s - 2 p
Method
Factorise the expression on the Rhs:
r = p ( 3 s - 2 )
Isolate the subject:
divide both sides of the equation by ( 3 s - 2 )
Solution
p = r /( 3 s - 2 )
Exercise
1. Make x the subject of the formula:
(i) t = x y + 3 x
......................................................
...................................................
x =.....................................
(ii) u = x - 4 x z
...................................................
...................................................
x =.....................................
(iii) w = 2x - x y ^2
....................................................
...................................................
x =.....................................
2. Make m the subject of the formula:
E = m v ^2 + m g h
.......................................................
m =..................................................
Solutions
1. (i) x = t / ( y + 3 )
(ii) x = u / ( 1 - 4z )
(iii) x = w / ( 2 - y^2 )
2. E = m ( 1/2 v^2 + gh )
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