Parentheses in advanced Order of Operations: Using parentheses

We solve the exercise in parentheses:

$3:9\cdot9-6=$

$\frac{3}{9}\cdot9-6=$

We simplify and subtract:

$3-6=-3$

We solve the exercise in parentheses:$3\cdot3+5:1=$

We place in parentheses the multiplication and division exercises:

$(3\cdot3)+(5:1)=$

We solve the exercises in parentheses:

$9+5=14$

First, we solve the exercise within the parentheses:

$4\cdot2-3:4=$

We place multiplication and division exercises within parentheses:

$(4\cdot2)-(3:4)=$

We solve the exercises within the parentheses:

$8-\frac{3}{4}=7\frac{1}{4}$

We begin by addressing the numerator of the fraction.

First we solve the division exercise and the exercise within the parentheses:

$400:(-5)=-80$

$(93-61)=32$

We obtain the following:

$\frac{-80-(-2\times32)}{4}=$

We then solve the parentheses in the numerator of the fraction:

$\frac{-80-(-64)}{4}=$

Let's remember that a negative times a negative equals a positive:

$\frac{-80+64}{4}=$

$\frac{-16}{4}=-4$

According to the order of operations, parentheses take precedence over everything else.

Therefore, we will first solve the multiplication and then addition within parenthesis.

To make solving the multiplication exercise easier, we will convert 8 into a simple fraction:

$2\times(3+\frac{1}{2}\times\frac{8}{1})=2\times(3+\frac{8}{2})=2\times(3+4)$

Now we will solve the addition exercise inside the parentheses and finally multiply to get our answer:

$2\times7=14$