02Krearrangingformulae

= Rearranging Equations =

In Science and Maths, many formulae are essential linear equations but have multiple pronumerals instead of numbers. It is common to have to rearrange these formula to get a particular pronumeral on its own.

The process is exactly the same as solving an equation (except that you are manipulating letters instead of numbers).


 * Make A the subject **

Making A (or any other letter) the subject of an equation involves rearranging the equation to get A on its own.

This means your equation will end up in the form A = ...


 * Example 1 **

The formula for converting temperatures from Fahrenheit (F) to Celsius (C) is math . \qquad C = \dfrac{5 \Big( F - 32 \Big) }{9} math

Make F the subject {ie rearrange to get the equation in the form F = ...}


 * Solution:**

math \\ . \qquad \dfrac{5 \Big( F - 32 \Big) }{9} = C \qquad \{ \; \times \;9 \;\} \\. \\ . \qquad 5 \Big( F - 32 \Big) = 9C \qquad \{ \; \div \; 5 \; \} \\. \\ . \qquad F - 32 = \dfrac {9C}{5} \qquad \;\; \{ \; + \; 32 \; \} \\. \\ . \qquad F = \dfrac {9C}{5} + 32 math


 * Example 2 **

The formula for the Surface Area of a cylinder is math .\qquad A = 2\pi r^2 + 2 \pi rh math

Make h the subject


 * Solution:**

math \\ .\qquad 2\pi r^2 + 2 \pi rh = A \qquad \{ \; - \; 2\pi r^2 \; \} \\. \\ . \qquad 2 \pi rh = A - 2 \pi r^2 \qquad \{ \; \div \; 2 \pi r \; \} \\. \\ . \qquad h = \dfrac{ A - 2\pi r^2}{2 \pi r} math


 * Example 3 **

The amount of energy (E) produced by a mass (m) if it is entirely converted to energy is given by math . \qquad E = mc^2 math

math . \qquad \text{where c is the speed of light} \\ . \qquad c \approx 3.0 \times 10^8 \; m/s math

Make c the subject


 * Solution:**

math \\ .\qquad mc^2 = E \qquad \{ \; \div \; m \; \} \\. \\ . \qquad c^2 = \dfrac{E}{m} \qquad \{ \; \text{square root} \; \} \\. \\ . \qquad c = \sqrt{ \dfrac{E}{m} } math .