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

##### 1 Answer

#### Explanation:

This is a trick question.

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

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

PParentheses.

EExponents.

MDMultiplication and Division - evaluated left to right.

ASAddition 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:

#6-:2*3#

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

#3*3#

which gives the final result

#9#

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

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.