# Totally Pointless, but I need a Mathmatician

The wife saw this on facebook,

6-1*0+2/2=?

She says the answer is 5
my phone calculator says the answer is 7
the computer calculator says the answer is 1

I can see how you get 1, but how do you get 5 or 7, what is the correct solution to this equation?

The order of operations rule says you resolve multiplication and division operations before addition and subtraction. So resolve 10 and 2/2 to get 6-0+1, and then resolve that to get 7. That’s the correct answer. Someone who did not learn “My Dear Aunt Sally” (Multiplication Division Addition Subtraction) might parse the operations left to right: 6-1 is 5, 50 is 0, 0+2 is 2, and 2/2 is 1.

I don’t really see a way to get to 5. Maybe 6-(1*0+2/2) ?

Yeah, that’s what I assumed - basically she’s incorrectly carrying over the subtraction.

But of course 7 is the right answer. OP: if your computer calculator is letting you put in the entire expression at once, then it’s garbage. But what I suspect is it’s a basic one that’s only allowing you to perform one operation at a time and you are chaining them. That’s user error in that you are not correctly applying the order of operations.

Oh, and I always learned it as “Please Excuse My Dear Aunt Sally” (parentheses & exponents being the first two). Of course, it’s slightly misleading in that multiplication/division and addition/subtraction are evaluated equally, but it doesn’t matter which of each pair you do first as long as you always do the M/D pair before the A/S pair.

There’s really no mystery about the computer calculator. In Windows, the calculator standard mode has no memory beyond the number on either side of the operator, so it gives the result based on the last 3 keystrokes: 2/2 = 1. But if you change it to scientific mode (where it really should be already), it gives the correct* answer of 7.

I just tried Mac OS calculator and it does 7 either way (but doesn’t show all your operations unlike Windows scientific calculator).

*Correct in the sense that this is the way that 99% of people can and should do it and if you insist otherwise you’re being pedantic and/or weren’t educated properly.

I agree with the others that the answer is 7 based on the established order of operations convention. Frankly, though, it’s arbitrary and it’s an artifact of our infix notation system. I see these sorts of posts often, and it frustrates me because it’s deliberately ambiguous, one of the great things about math is it shouldn’t be. Sometimes I’ll add unnecessary parentheses with formulae just for the sake of clarity, either because it prevents someone from accidentally making an order of operation mistake, or it helps one intuitively understand why a certain operation is there.

The people who get 5 are taking PEMDAS too literally and doing addition before subtraction.

So they’re doing:
6-1*0+2/2
6-0+1
6-(0+1)
6-1
5

There’s some other image circulating Facebook (Only a genius will get this!) that does the same thing.

Holy crap, I got it right, and I’m a math dumbass. Thank you, dear Aunt Sally!

I can’t imagine anyone writing the equation in the OP without parentheses except on a test covering order of operations.Parentheses provide clarity.

My mnemonic was Please Execute My Dumb Ass Sister

That’s not doing addition before subtraction though. That’s multiplying that term by negative one.

If you use the Windows calculator in its standard format, you get the incorrect answer of 1. But what a lot of people don’t know is that you can change the calculator’s format. If you switch to scientific, you get 7.

Pull up the calculator, and click View. That gives you several different options.

I did not learn MDAS so I came up with 7. Doing it MDAS gives me 5. 1*0=0, 2/2=1, 0+1=1, 6-1=5

And of course Windows calculator is emulating the various physical calculators that are available. The simplest, cheapest calculators perform all operations immediately, in the order you type them in, while the more sophisticated calculators (scientific and graphing calculators) follow the rules for the order of operations.

My son got it right. He’s in 4th grade. They covered this earlier this year.

I can’t think of a logical reason to do it but if you do addition and subtraction first and the multiplication and division you’ll get 5.

well when I put it into each calculator, I input the equation exactly as typed in the OP. The computer calc has basic mode, engineer mode, date calculator, conversion, and degree calc. I know how to use basic, never had a reason to look at date calculator, haven’t needed conversion mode, and wouldn’t know how to use engineer or degree mode.

I swear to God I never learned (or more likely forgot it was so long ago) order of operations rule

The mrs. says yes she screwed up on the subtraction step

Well, it’s not like it’s a one-off thing you learn once and then move on. It’s a very fundamental part of basic arithmetic, and literally all math anyone will ever do in school past the 2nd or 3rd grade relies on knowing the correct order of operations. You simply cannot do any sort of math properly without knowing it.

The fact that anyone would be passing something so basic around FB as a “tricky” sort of problem is incredibly alarming. If those same people were also able to pass middle school (and God forbid anything beyond that), then our educational system has really–spectacularly and miserably–failed.

I disagree. The expression of the OP is not really one that you ever see in math class. Most of the time, multiplication is implied by juxtaposition or parentheses, and division is marked by a fraction bar, making the order of operations that much more clear. With these “text” sort of expressions, those clues are missing, and you are forced to resort to a precise, and oft forgotten, understanding of the order of operations.

For example, 12/2/3 evaluates to 2, because you are supposed to do the left-most division first. In a math text, though, one of the fraction bars will be written larger than the other one, giving something like 12/[SUP]2[/SUP]/[SUB]3[/SUB] (= 18) or [SUP]12[/SUP]/[SUB]2[/SUB]/3 (= 2), making the order to follow a bit more obvious.