Rearranging Equations

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 3a = b to have a on its own c and 3 need to be on the other side of the ‘=‘ apply the inverse functions. c a = b 3 × 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 a x y = b Divide on one side of the equation goes to multiply on the other side a x y = 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 y = b - a • 1. a + y = b • 2. y – c = d • xy = z • e + 2y = f • 2l + 5y = m • 3y = h + i y = d + c y = z x y = f - e y = m – 2l y = h + i 2 3 5

Rearranging Equations