sknox (2/6/2013)
Always work left-to-right -- don't give precedence to an operation on the same level.For example, take
8 / 4 x 2
The correct way is left-to-right:
8 / 4 = 2 x 2 = 4
If we do division first, we get the same answer, as it's still left-to-right. But if we do multiplication first, we get:
8 / (4 x 2 = 8) = 1
It's the difference between
8
-- x 2
4
and
8
-------
4 x 2
I agree you should always work from left to right for the avoidance of doubt. But (as long as you don't add brackets in your head), the order you carry out multiplication and division doesn't actually make a difference to the result. In your example:
8 / 4 x 2
is the same as
8 x 2 / 4
or
2 / 4 x 8
Calculating the 4 x 2 part first is invalid because you are changing the 2 from a numerator to a denominator. It's not the order in which you carry out the operations that matters, as long as you carry out the correct operations!
8 x 2 / 4 x 3 / 2 x 5 / 10
is the same as
8 x 5 / 2 x 3 / 10 x 2 / 4
is the same as
5 / 2 x 8 x 3 / 4 / 10 x 2