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

Apr 17, 2016

$9$

#### Explanation:

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:

$\left(1 + 2\right) = 3$.

Then we have:

$6 \div 2 \cdot 3$

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

$3 \cdot 3$

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 $1$.

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.