Math and Order

The Problem

I’m sure you’ve seen math questions like this on Facebook:

3 + 5 x 4 + 2 = ?

What is the answer? The problem is that there is no “the” answer. It all depends on the order of precedence you learned in school.

The order of precedence lays out which part of the equation you handle first. Basically, it tells you where to put the missing parentheses. I’ve identified four methodologies promoted by mathematicians and logicians.


My favorite, but least practical approach, is to declare the equation logically invalid due to the ambiguity. Moving on.


Next is the method I learned in school, so I assume it is the correct way. Parts of the equation are handled in the order of the operator; multiplication, division, addition then subtraction. (I included just the basic binary operators for simplicity.)

So the equation would be treated like this: 3 + (5 x 4) + 2 = 25

Left To Right

Another method that people learned in school is to handle the equation left to right. This would result in: ((3 + 5) x 4) + 2 = 34

In The Middle

The last method I found was described on a single website. I found no corroboration, but also found nowhere that explains why it’s wrong. With this method you start in the middle and work outward. That gives you: (3 + 5) x (4 + 2) = 48

The Real Problem

Ask yourself; Why are people posting these math problems in the first place? Because they are trying to identify people who think they are so much smarter than other people to the point that they don’t notice they are being manipulated.

The poster doesn’t really care what you think the answer is. They’re looking for people at which to launch advertising or phishing attempts.

So, the best answer is not to play.


Turns out the “start from the middle” method was a misinterpretation of how quadratic equations are handled. I’m leaving it in though. It’s funny.