Rearranging Equations Rearranging equations is based upon inverse functions The four mathematical operations are in pairs: + , - Add and subtract operations are opposite to each other (inverse functions) × , ÷ multiply and divide operations are opposite to each other (inverse functions)

Rearranging Equations The basic principal for rearranging equations is to look at the operation that applies to a number or variable apply the inverse function to move it to the other side of the equation Example: to move the 3 to the other side of the ‘=‘ apply the inverse function. x + 3 = y The function is ‘+’, so the inverse function is ‘-’ x = y + 3 -

Rearranging Equations Example: to move the 3 to the other side of the ‘=‘ apply the inverse function. 3x = y The function is ‘×’, so the inverse function is ‘÷’ x = y 3 × _ Rearrange this equation to make a the subject of the formula to have a on its own c and 3 need to be on the other side of the ‘=‘ apply the inverse functions. 3a = b c 3 a = b × c Writing the equation like this with a = something is called making a the subject of the formula c ÷ 3

Rearranging Equations To summarise: Multiply on one side of the equation goes to divide on the other side x y = a b Divide on one side of the equation goes to multiply on the other side x y = a b Add on one side of the equation goes to subtract on the other side x = y + 3 - Subtract on one side of the equation goes to add on the other side x = y - 3 +

Rearranging Equations Now try these: Rearrange these to make y the subject of the formula 1. a + y = b 2. y – c = d xy = z e + 2y = f 2l + 5y = m 3y = h + i y = b - a y = d + c y = z x y = f - e 2 y = m – 2l 5 y = h + i 3