How do you simplify #6÷2(1+2)# usind PEMDAS?

1 Answer
Apr 17, 2016




This is a trick question.

If you apply PEMDAS strictly with no embellishments then the answer is #9#.

PEMDAS is a mnemonic for the following conventions of order of operations:

P Parentheses.

E Exponents.

MD Multiplication and Division - evaluated left to right.

AS Addition and Subtraction - evaluated left to right.

Note that multiplication and division have the same priority and addition and subtraction have the same priority.

In our example, we first evaluate the parenthesized expression:

#(1+2) = 3#.

Then we have:


which is evaluated left to right, so next the division gives:


which gives the final result


This is one instance in which following PEMDAS strictly gives an unexpected result. I think most people would somehow give the multiplication higher priority, resulting in the answer #1#.

PEMDAS is meant to help reduce ambiguity, but in instances like this the original expression should be given extra parentheses to make it intuitive and unambiguous.