# How do you simplify 48÷2(9+3)  using PEMDAS?

Apr 17, 2016

$288$

#### Explanation:

This is a trick question.

If you apply PEMDAS strictly with no embellishments then the answer is $288$.

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.

So in our example:

$48 \div 2 \left(9 + 3\right) = 48 \div 2 \cdot 12 = 24 \cdot 12 = 288$

The nasty thing with this example is that the multiplication by juxtaposition of the $2$ and $\left(9 + 3\right)$ is visually 'closer' than the division using the obelus $\div$, so looks more 'binding'.

In fact PEMDAS does not distinguish between this multiplication by juxtaposition and any other multiplication, so it will be evaluated at the same level of priority as the division, left to right.

If the writer of the original expression wanted to be clear they should have added parentheses.