I've always heard it that way too but I think it is for consistency with students, imo
Logically, if you are looking at division = multiplying by inverse and subtraction = adding the negative, you should be able to do it both ways. Addition and multiplication are both associative, so we can do 1+2+3 = (1+2)+3 = 1+(2+3) and get the same answer.
But subtraction and division are not associative. Any time you work on paper, 2 - 2 - 2 would equal -2. That is, (2-2)-2=0-2=-2. If you evaluate right to left, you get 2-2-2=2-(2-2)=2-0=2
Correct, subtraction and division are not associative. However, what is subtraction if not adding the opposite of a number? Or division if not multiplying the inverse? And addition and multiplication are associative.
2-2-2 can be written as 2 + (-2) + (-2) which would equal -2 no matter if you solve left to right, or right to left.
In your example with the formula from right to left, distributing the negative sign reveals that the base equation was changed, so it makes sense that you saw a different answer.
2 - (2 - 2) = 2 + ((-2) + 2) = 2
2-(2-2)
But you broke the rule of left-associativity there. You can go right to left provided you keep each number with the sign to it's left (and you didn't do that when you separated the first 2 in brackets from it's minus sign).
I've always heard it that way too but I think it is for consistency with students, imo Logically, if you are looking at division = multiplying by inverse and subtraction = adding the negative, you should be able to do it both ways. Addition and multiplication are both associative, so we can do 1+2+3 = (1+2)+3 = 1+(2+3) and get the same answer.
But subtraction and division are not associative. Any time you work on paper, 2 - 2 - 2 would equal -2. That is, (2-2)-2=0-2=-2. If you evaluate right to left, you get 2-2-2=2-(2-2)=2-0=2
Correct, subtraction and division are not associative. However, what is subtraction if not adding the opposite of a number? Or division if not multiplying the inverse? And addition and multiplication are associative.
2-2-2 can be written as 2 + (-2) + (-2) which would equal -2 no matter if you solve left to right, or right to left.
In your example with the formula from right to left, distributing the negative sign reveals that the base equation was changed, so it makes sense that you saw a different answer.
2 - (2 - 2) = 2 + ((-2) + 2) = 2
But you broke the rule of left-associativity there. You can go right to left provided you keep each number with the sign to it's left (and you didn't do that when you separated the first 2 in brackets from it's minus sign).