# What is 6-:2(1+2), using order of operations?

Mar 11, 2018

Ambiguous

#### Explanation:

Order of operations is PE (MD) (AS). So we start with parenthesis.

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

Now this is ambiguous. Multiplication and division now have to happen at the same time, so we don't know if this means either of these:
$\frac{6}{2 \cdot 3} = \frac{6}{6} = 1$

or

$\frac{6}{2} \cdot 3 = 3 \cdot 3 = 9$.

Mar 11, 2018

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

#### Explanation:

Regardless of the way in which the order of operations is written, it always follows the same structure; Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
Follow the order, we see that the parentheses (brackets), must be completed first.
$1 + 2 = 3$
Our new expression is $6 \div 2 \cdot 3$.
The only remaining operators are multiplication and division so we proceed in the order in which the occur. The division is the first operator we come across reading from left to right. Completing this, we are left with the following:
$3 \cdot 3$
The expression can now be solved as $3 \cdot 3 = 9$.