I check my 12-year-old son’s math homework every night, and lately he’s been neck-deep in the Order of Operations. This is the order in which you do smaller stuff in a larger problem. For instance:
3 + 5 * 7 / (8 – 7)
In this case, you need to do the 8 – 7 first since it’s in parentheses, then the 5 * 7, and the result should be divided by the 1 from the parenthetical operation then add to the three. So it goes like this:
3 + 5 * 7 / 1
3 + 35 / 1
3 + 35
The answer for the above problem is 38.
The mnemonic for this is:
Excuse (exponent operations)
My Dear (multiplication and division)
Aunt Sally (addition and subtraction)
So, here’s my question —
Why is this the order of operations? This has been so designated as the way we’re supposed to do it, but why? Why does addition and subtraction come before multiplication and division? Who made the rule and why? There are two possibilities:
- Someone just decided this and it stuck because we all needed a consistent way of doing it.
- There is some higher mathematical truth to it, and at some base level this is the only way to do it because of some core logical principle.
So, which is it? Does anyone know? I’d be interested if this is just an arbitrary (but necessary) decision someone made.