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I was just surfing a social site and found this question posted by someone. People were arguing or different answers like 80, 100, 120. So, what is the correct answer for $10 \times 10-10+10$?

I used order of operations (BODMAS) and got that the answer is 100. Am I right?

Caleb Stanford
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AR SMARTY
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  • It depends on what convention you use, that's why those sort of questions does not make sense as is. – servabat Jan 09 '15 at 13:49
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    @servabat: No, the convention is unambiguous in this case. (You can even change the number-system base and the answer is the same!) – TonyK Jan 09 '15 at 14:08
  • @TonyK : of course not, if I state in my convention you go with additions first and multiplication last, the answer is different. – servabat Jan 09 '15 at 14:10
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    @servabat: Well, you could also decide that in your convention, the digit $1$ represents the number seven. But that is very unusual. Here is a rule that you might find useful in everyday life, as well as mathematics: Unless otherwise stated, normal conventions apply. – TonyK Jan 09 '15 at 14:33
  • @TonyK : because they are normal in your work environment does not mean they are everywhere, and yet it's why these questions are somehow 'trended'. Every single guy would come with its answer and think it's the only valid one, so people that post it would get a lot of comments and stuffs which is exactly their goal. – servabat Jan 09 '15 at 14:44

4 Answers4

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The usual convention is to give addition and subtraction equal precedence, evaluating them from left to right. So we start with multiplication ($10 \cdot 10$), then do the addition and subtraction from left to right to get $(100 - 10) + 10 = 100$.

If we were to take the acronym PEMDAS (BODMAS, BIDMAS, etc.) literally, it would seem that addition should be evaluated before subtraction. In this case we would get $10 \cdot 10 - 10 + 10 = (10 \cdot 10) - (10 + 10) = 80$. But this would not be correct; despite A being listed before S in the acronym, the intention is that they be given equal precedence and evaluated left to right.

Caleb Stanford
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  • Execution order from left to right is actually not required at all. Subtraction and addition have the exact same priority, because subtracting = adding a negative number, and we know we can add numbers in any order and still get the same result. You can add -10 and +10 to each other before adding it all to the 100. – Slava Feb 01 '17 at 13:03
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It can be interpreted as an abbreviation of: $$(10.10+(-10))+10$$ as well as an abbreviation of: $$10.10+((-10)+10)$$ In both cases we find:

  • $(10.10+(-10))+10=(100+(-10))+10=90+10=100$
  • $10.10+((-10)+10)=100+0=100$

So our final conclusion is: $$10.10-10+10=100$$ No ambiguity arises, wich is a consequence of the fact that addition is associative.

Vera
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Its 100. You will first execute the multiplication and then the minus and plus.

uitty400
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$$ 10 \cdot 10-10+10 = 100 - 10+10 = 90 +10 = 100. $$

Multiplication first, then addition and subtraction in the order they appear left to right is what you get by applying PEMDAS.

Caleb Stanford
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Batman
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