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Manipilating Equations

You need to manipulate equations so that the unknown is alone on the left and all of the known values are arranged on the right. You can then insert the numbers and use your calculator to calculate the answer.

The golden rule is:

'Do unto one side that which thou dost to the other'

Multiplying, dividing, squaring, cubing, rooting the whole of both sides of the equation is allowed, as is adding or subtracting the same amount to each side.

You can think of an equation as a see-saw with equal loads on each side.

Changing the load on each side in the same way therefore still results in balance.

eg.

X + 2 = 5

Subtract 2 from each side to get X alone and you get

 

X = 5 - 2 = 3

----------------------------------------------------------------------

4x = 8

can be solved by dividing each side by 4

x = 2

  • If you move a number multiplying one side to the other you have to divide the other side by it and vice versa (cross multiplication)
  • If a number is added to one side you have to subtract it from the other side.
  • A fraction is unchanged if you multiply/divide the top and bottom by the same number
(NB you can't to that with addition/subtraction)