I keep seeing this on Facebook, and for whatever reason, everyone is getting a different answer. Let’s take a look at this problem, and figure out the correct answer.
If you remember back to elementary school, there was this thing called the order of operations (OoO). For the sake of this problem, we only need to know a very small portion of the OoO:
- Multiplication comes first
- Addition and subtraction come second
- Operations are performed by level from left-to-right, starting with the highest level first (so, left-to-right with multiplication, then left-to-right with addition/subtraction)
Let’s walk through those three steps.
Since there are no parentheses, the multiplication that happens in this equation only applies to the preceding number. So, to make this simple, let’s stub-in parentheses where they would go if we wanted to be verbose:
It is not this:
The end result becomes:
Now that multiplication is out of the way, we can perform addition and subtraction. Something to keep in mind, unless there are parentheses, addition and subtraction have the same weight. By that, I mean you start from the left, go right, and perform them in the order you encounter. To make this simpler, let’s convert that pesky subtraction into an addition:
All that’s left is to add them all together:
(1+1+1+1+1+1+1+1+1+1+(-1)+1+1+1+1+1)+(0) = 14
If you want to double-check, you can always check with one of the smartest math-engines out there: WolframAlpha. According to him, it looks like we did this right!
Moral of the Story
Anytime you get a “tricky” math problem, just remember your order of operations and you’ll be fine.