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

Mar 26, 2016

$6 \div 2 \left(1 + 2\right) = 9$

#### Explanation:

This is an interesting problem and may be a trick question.

The visual grouping of the $2$ with the $\left(1 + 2\right)$ makes it look like this multiplication should have higher priority than the preceding division, but according to PEMDAS it doesn't.

To see slightly more clearly what the issue may be, try writing the multiplication explicitly to get:

$6 \div 2 \times \left(1 + 2\right)$

Secondly, note that the PEMDAS mnemonic does not give greater priority to multiplication over division. It actually expands out as:

P for Parentheses

E for Exponents

MD for Multiplication and Division (left to right)

AS for Addition and Subtraction (left to right)

So if we explicitly follow PEMDAS we find the following:

Dealing with the parenthesis first, we evaluate the expression $1 + 2$ it contains to get: $\left(1 + 2\right) \to 3$, hence:

$6 \div 2 \times \left(1 + 2\right) = 6 \div 2 \times 3$

Then evaluate this left to right (since multiplication and division have the same priority):

$6 \div 2 \times 3 = \left(6 \div 2\right) \times 3 = 3 \times 3 = 9$