Originally Posted by dan330
but the way it is represented... there is an implied reason for the location....
so there is an implied () around the first part = (6) ..
and an implied () around the second part = (2(1+2))..
you can not change what is inside or outside ().
NOTE: that is my interpretation of "implied"... i can be wrong.
is there an expert / professor here that can state the facts?
I'm no professor, but this is what I think it comes down to: To change the order of operations around the adition part (1+2) you need to add a parenthesis to make that go first, we all agree there.
But it shouldn't (and doesn't in my mind) make any sense that I should have to infer
that a number that is near a parenthesis should have it's order of operation changed too. The parenthesis should change only
what's inside it, with the innermost being evaluated first.
Basically some other problems to illustrate:
we clearly know that 6 * (1+2) = 18
And that 6 * 1 + 2 = 8
And that 6 / (2(1+2)) = 1 <- this is clear and obvious
^ So how is it we can infer 6 / (2(1+2)) from 6/2(1+2) ?
Unless there's some clear exception to the order of operations rule, we should not make assumtions that require additional parenthesis (imo)
Though my own argument can be used against me here too because the opposing argument could be how can you infer (6/2) * (1+2) ?
IMO,the reason you can infer the second (6/2) * (1+2) is because 6/2 doesn't need parenthesis normally, as it would natually come first in the order of operation.
6/2*3 is certainly clear enough I think. Once the parenthesis have been evaluated, they shouldn't affect the rest of the equation.
Also, I think It's pretty clear that:
And that's my final proof. Irrefutable! Just be sure to evaluate the (imo) first.