What is $10 \times 10-10+10$?

Question

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?

Answer 1

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

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

Answer 2

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

Answer 3

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.

Answer 4

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.