Occasionally you will see simple math problems posted on Facebook or other social networks with problems that look easy to solve, but test your understanding of algebraic operators. One such post is:

3 + 3 x 3 – 3 + 3 =

This was asked today and there were several results that came back. The answer is of course 12. How so? Well if we use algebraic operators, the multiply comes first. It helps to use parenthesis to show the proper groupings….

3 + (3 x 3) – 3 + 3 = 3 + 9 – 3 + 3 = 12.

We can quickly see the -3 and the +3 cancel each other out so you really end up with 3 + 9 or 12. Well how did people come up with other values like 6, 15 and 18? Again, it has to do with groupings. Since there were no parenthesis in the original problem, multiply and divide operations come first, left to right, then the add and subtract operations happen second. Let’s get to the other numbers, which would be right if parenthesis were involved.

3 + (3 x 3) – (3 + 3) = 3 + 9 – 6 = 6

(3 + 3) x 3 – 3 + 3 = 6 x 3 – 3 + 3 = 18

3 + 3 x (3 – 3 )+ 3 = 3 + 3 x 0 + 3 = 6

With the parenthesis, these would be the right answers. Honestly I couldn’t come up with a quick path to 15. But since the original equation did not use these grouping methods, only the first option is mathematically correct.