GCSE Maths - Changing the Subject of a Formula

Rearranging Formulae Why rearrange formulae? The formula d = st expresses distance (d), in terms of speed (s) and time (t).

It is sometimes necessary 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 single variable 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 .

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(ii) v = 3 x - 4 tz ....

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. (iii) s = (t/p) - 2r .

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. 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 original formula, we need first to collect 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 .
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(ii) u = x - 4 x z .
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(iii) w = 2x - x y ^2 .

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2.
Make m the subject of the formula: E = m v ^2 + m g h ..
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m =.

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. 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 )