Had a debate on whether you could do addition/subtraction in any order you want. Specifically, for the following:
$9 – 4 + 3$
We both agree that the answer is 8.
I argue that, by giving addition a higher priority than subtraction (rather than the same priority and going left-to-right), you would end up with $9 – 4 + 3 = 9 – 7 = 2$, which is an incorrect answer, and therefore it matters that addition and subtraction have the same priority.
The other person argues that the order of operations doesn't matter and that it can be done in any order, as by giving addition a higher priority than subtraction, you would end up with $9 – 4 + 3 = 9 + (-4 + 3) = 9 + – 1 = 8$, which is the correct answer, and therefore it wouldn't matter if addition/subtraction had different priorities rather than the same.
I'm arguing that bringing the $- 4$ inside the bracket and then performing it before the $+ 3$ wouldn't be done if addition had a higher priority. The fairly long, debate can be seen here if you want to read it, so I don't paraphrase it all and bias my side too much.
My overall question is who is correct; does the order of operations matter with just addition and subtraction? I'm willing to accept answers for either side, so long as they give a reason.
Best Answer
Let's clarify:
$$9 - 4 + 3 \color{red}{\ne} 9 - (4 + 3) \tag{1}$$
It appears that you are confusing what is means to group together, or associate, the operations.
BUT, the mistake in the statement $(1)$ above is that the terms haven't been grouped correctly. The correct way to associate the latter two terms is:
$$\begin{align*}9 - 4 + 3 &= 9 + (-4 + 3) \tag{2}\\ &=9-(4-3) \end{align*}$$
In the original statement $(1)$ at the top of this post, what you have done is introduced a second minus sign.
$$\color{red}{9 - (4 + 3) = 9 - 4 - 3} \tag{3}$$
To conclude, there is no ambiguity to what either $(2)$ or $(3)$ means. But they mean completely different things. The parenthesis, used for grouping in this example, must adhere to the multiplicative property of distribution. If we stick parenthesis into a math statement at will, then we run the risk of completely altering the results. To group items properly, we must make sure that our result conveys the same message - the same order of operations.