Parentheses in advanced Order of Operations: Using parentheses

Let's solve this problem step by step using the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction):

1. First, let's focus on what's inside the parentheses: $\sqrt{36}+9$

2. We need to evaluate the square root first:

• $\sqrt{36} = 6$ (because $6 \times 6 = 36$)

3. Now our expression looks like this: $2\times(6+9)$

4. Next, we perform the addition inside the parentheses:

• $6 + 9 = 15$

5. Our expression is now: $2\times15$

6. Finally, we perform the multiplication:

• $2 \times 15 = 30$

Therefore, $2\times(\sqrt{36}+9) = 30$

This matches the provided correct answer of 30.

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 solve the exercise in parentheses:

$3:9\cdot9-6=$

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

We simplify and subtract:

$3-6=-3$

According to the rules of the order of operations, we first solve the exercise within parentheses:

$4+5=9$

Now we obtain the exercise:

$2\times3-9:2=$

We place in parentheses the multiplication and division exercises:

$(2\times3)-(9:2)=$

We solve the exercises within parentheses:

$2\times3=6$

$9:2=4.5$

Now we obtain the exercise:

$6-4.5=1.5$

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:

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

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

First, we solve the exercise within the innermost parentheses:

$(26-6:3)=$

According to the order of operations, we first divide and then subtract:

$26-2=24$

Now we obtain the exercise:

$225:(24\times5)=$

We solve the multiplication exercise and then divide:

$225:120=1.875$

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

Inside the parentheses, we will first solve the multiplication problem and then add.

To make solving the multiplication problem easier, we will convert 8 to 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 problem inside the parentheses and finally multiply:

$2\times7=14$