The answer is -4. You do addition left to right. You wouldn't do 12 + 7 = 19 then subtract from 1. That would be right to left. We just want to
subtract the 12 from 1. We don't want to subtract the 12 plus subtract 7 more. We want to add 7 more. You would subtract 12 from 1 first which would
be -11 and then add the 7 which equals -4.
As long as you're using + and - as instructions, the instructions must be carried out in order. If you want to do it commutatively and move the
numbers around then you have to make sure you're moving the number's SIGN with it as well.
The positive + sign symbols on numbers are usually missing. Only when it's negative do you put the -. So, people start thinking + and - are
instructions and that + means to add and - means to subtract, but they're not instructions. They're supposed to be used as labels. They tell you what
the number's sign is.
Don't get tricked by it though. Just put the missing sign symbols back in yourself and all becomes clear. For every number that doesn't have an - next
to it, just put a + next to it.
+1, -3, +4, +7. When you do math this way you NEVER subtract. You multiply the numbers first, and then add up the remaining terms, but you'll be
adding negative numbers so you get the same results. Plus and minus signs are no longer instructions for you to do something, but now have been turned
into labels that tell you what each number's sign is. So, the equation you actually have is this.
+1 plus -3 times +4 plus +7.
Multiplication first. -3 x +4 = negative 12.
This is where some are getting tripped up. By saying +12 + 7 = 19. But that's wrong! THERE IS NO +12! The 12 we have is a -12, not a +12. We got -12
from multiplying a NEGATIVE 3 times a positive 4. The correct answer here is -12 + 7 = -5 and not 19.
So now you have a positive 1 and a negative 5. You can ADD the -5 to +1 and you'll get -4. The correct answer.
This is actually the right way to do addition because there is no such thing as subtraction. Doesn't exist! Only addition exists. You always just add
up all the numbers. Subtraction is just the addition of the negative numbers. Anytime you see an - sign don't say minus to yourself. Say plus negative
so you know which number the - belongs to. 1 - 3 is 1 plus negative 3.
edit on 13-10-2010 by tinfoilman because: (no reason given)