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)