Rearranging Formulae

Key facts and exam tips

• A formula is a way of describing a mathematical relationship. The letters in a formula are called variables. A formula connects two or more variable terms and may include numbers (called constants) as well.
  
• The letters chosen in a formula often relate to the thing that they represent. For example, volume is usually expressed as V, height would be called h and t is often used to denote time.
  
• If a formula is written so that one letter is on one side of the equals sign and all the other letters and numbers are on the other side, then that letter is called the subject of the formula (ie one variable - the subject - is expressed in terms of all the other variables).
  
• Changing the subject of a formula involves rearranging it using algebra so that a different letter appears on its own on one side.
  
• Inverse operations are needed to rearrange a formula. The inverse of addition is subtraction. The inverse of multiplication is division. The inverse of squaring is to take the square root.
  
• When rearranging you need to think about the order in which you would perform the operations in the original formula. To rearrange you need to reverse this order and perform the opposite (inverse) operation. It's like working backwards through each step in the calculation.
  
• The inverse operation is applied to both sides of the formula and will 'cancel out' on one side.
  
• Remember to use brackets if you want to show that the whole of one side is multiplied or divided by a term.
  
• It is usual to write the formula with the subject on the left. After rearranging you can flip the formula around if necessary, so that it reads in a natural way from left to right.
  
• Remember that you will have changed the subject only when you have got the variable given in the question on its own (and positive, not negative) on one side of the formula with all the other variables and numbers on the other side.
  
• Examination questions often ask you to substitute into or evaluate a formula as well. This means that you will replace letters with values (given in the question) and work out a numerical answer.
  
• Don't try to rearrange a formula entirely in your head. It is better to show each step in your working and demonstrate to the examiner that you understand how to use inverse operations to 'undo' each part of the formula in a logical manner.