Change of Subject of Formulae (Transposition of Formulae)

To change or transpose a formulae means to rearrange it so that a different letter or symbol becomes the subject. This process is exactly the same as solving equations.

Remember, what is done to the LHS is done to the RHS of the formulae at all times.

e.g.   I  = \( \frac{PRT}{100} \)

Make P the subject of the formula

Multiply both sides by 100

⇒ \( \scriptsize 100 \: \times \: I = \frac{PRT}{100} \scriptsize \; \times \; 100 \)

⇒ 100I  = PRT

Divide both sides by RT

⇒ \( \frac{100I}{RT} = \frac{PRT}{RT}\)

⇒ \( \frac{100I}{RT} = \frac{P\not{R}\not{T}}{\not{R}\not{T}}\)

P = \( \frac{100I}{RT} \)

Worked Example 8.2.1:

Make x the subject of formulae of Questions 8.2.1 a – d

a. y = x + 6
b.   x²  =  10 – y
c. \( \frac{x}{5} \scriptsize = a + 2x \)
d. y = \( \scriptsize 5 \left(\sqrt{x^2 \: + \: 2}\right) \)
e. Make T the subject of the formula: P = \( \frac{nRT}{V} \)
f. Make m the subject: w = \( \sqrt {\frac{K}{m}} \)
g. T = \(\scriptsize 2 \pi \sqrt {\normalsize \frac{L}{g}}\) make  g the subject

Solution

a. y = x + 6

Subtract 6 from both sides

y – 6 = x + 6 – 6

Move x (the subject) to the left-hand side

x + 6 – 6 = y – 6

x + 0 = y – 6

x = y – 6