The problem with problems

This maths problem has hit the pages of Facebook recently:

6^2 / 2(3) + 4

There seems to be a particular problem with what to do with the brackets.  Before we look at that, lets agree on what we can.

6^2 (6 squared) = 36

(+ 4) indicates simply that we add 4 at the end.

So the problem area is 2(3)

Some people say that the brackets merely indicate “multiply”.  They also say that because there is no operator inside the brackets that that area of the problem does not attract any special precedence. This is in spite of the BODMAS/PEMDAS rule that says that brackets take the highest priority.

I say that the brackets mean far more than that.  They mean “multiply whatever is in the brackets by the figure (if any) immediately to the left of the brackets”.  The number immediately to the left of the brackets “belongs” to the brackets.

Let’s take a look at a slightly different problem.

2(2+1) = 6

Agreed?  Inside the brackets we have (2 + 1) = 3, and we have two lots of those.

Suppose we say that the brackets merely indicate “multiply”, could be get rid of the brackets and replace them with a multiplication sign?

2 * 2 + 1 = 5 (remember, in the rules of precedence the multiplication is dealt with first, before the addition.

So, 2(2+1) = 6 then.  But I’d like to simplify that a little.  How does 2(3) = 6 look?  It’s just the same as the expression at the top of the page, isn’t it?

So, going back to the original problem:

6^2 / 2(3) + 4

6^2 = 36

2(3) = …well the 2 “belongs” to whatever is inside the bracket, so 2(3) = 6

36 / 6 = 6

…add 4

6+4 = 10

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