Advanced Order of Operations Worksheets - Math Monks - Free Printable

To solve the given problems, we will follow the order of operations (PEMDAS/BODMAS rules):

1. Parentheses/Brackets
2. Exponents/Orders
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Let's solve each problem step by step.

---

Problem 1:

\[
-6 + (-3 - 3)^2 \div 3
\]

#### Step-by-Step Solution:
1. Solve the expression inside the parentheses:
\[
-3 - 3 = -6
\]
So the expression becomes:
\[
-6 + (-6)^2 \div 3
\]

2. Calculate the exponent:
\[
(-6)^2 = 36
\]
So the expression becomes:
\[
-6 + 36 \div 3
\]

3. Perform the division:
\[
36 \div 3 = 12
\]
So the expression becomes:
\[
-6 + 12
\]

4. Perform the addition:
\[
-6 + 12 = 6
\]

#### Final Answer:
\[
\boxed{6}
\]

---

Problem 2:

\[
\frac{2 + 4(7 + 2^2)}{4 \times 2 + 5 \times 3}
\]

#### Step-by-Step Solution:
1. Solve the expression inside the parentheses in the numerator:
\[
7 + 2^2 = 7 + 4 = 11
\]
So the numerator becomes:
\[
2 + 4 \times 11
\]

2. Perform the multiplication in the numerator:
\[
4 \times 11 = 44
\]
So the numerator becomes:
\[
2 + 44 = 46
\]

3. Solve the denominator:
\[
4 \times 2 + 5 \times 3
\]
Perform the multiplications:
\[
4 \times 2 = 8 \quad \text{and} \quad 5 \times 3 = 15
\]
So the denominator becomes:
\[
8 + 15 = 23
\]

4. Divide the numerator by the denominator:
\[
\frac{46}{23} = 2
\]

#### Final Answer:
\[
\boxed{2}
\]

---

Problem 3:

\[
(5 + 9 - 10) \times 6 + 4 - 2
\]

#### Step-by-Step Solution:
1. Solve the expression inside the parentheses:
\[
5 + 9 - 10 = 14 - 10 = 4
\]
So the expression becomes:
\[
4 \times 6 + 4 - 2
\]

2. Perform the multiplication:
\[
4 \times 6 = 24
\]
So the expression becomes:
\[
24 + 4 - 2
\]

3. Perform the addition and subtraction from left to right:
\[
24 + 4 = 28
\]
\[
28 - 2 = 26
\]

#### Final Answer:
\[
\boxed{26}
\]

---

Problem 4:

\[
\frac{-5^2 + (-5)^2}{(4^2 - 2^5) - 2 \times 3}
\]

#### Step-by-Step Solution:
1. Solve the numerator:
\[
-5^2 + (-5)^2
\]
Calculate each term:
\[
-5^2 = -(5^2) = -25 \quad \text{and} \quad (-5)^2 = 25
\]
So the numerator becomes:
\[
-25 + 25 = 0
\]

2. Solve the denominator:
\[
(4^2 - 2^5) - 2 \times 3
\]
Calculate each term:
\[
4^2 = 16 \quad \text{and} \quad 2^5 = 32
\]
So:
\[
4^2 - 2^5 = 16 - 32 = -16
\]
Now calculate the rest of the denominator:
\[
-16 - 2 \times 3 = -16 - 6 = -22
\]

3. Divide the numerator by the denominator:
\[
\frac{0}{-22} = 0
\]

#### Final Answer:
\[
\boxed{0}
\]

---

Problem 5:

\[
5 + 2^3 \times (22 \div 11) - 3^2 \times (4 + 5)
\]

#### Step-by-Step Solution:
1. Solve the exponents:
\[
2^3 = 8 \quad \text{and} \quad 3^2 = 9
\]
So the expression becomes:
\[
5 + 8 \times (22 \div 11) - 9 \times (4 + 5)
\]

2. Solve the expressions inside the parentheses:
\[
22 \div 11 = 2 \quad \text{and} \quad 4 + 5 = 9
\]
So the expression becomes:
\[
5 + 8 \times 2 - 9 \times 9
\]

3. Perform the multiplications:
\[
8 \times 2 = 16 \quad \text{and} \quad 9 \times 9 = 81
\]
So the expression becomes:
\[
5 + 16 - 81
\]

4. Perform the addition and subtraction from left to right:
\[
5 + 16 = 21
\]
\[
21 - 81 = -60
\]

#### Final Answer:
\[
\boxed{-60}
\]

---

Problem 6:

\[
\{[-9 - (2 - 5)] \div (-6)\}
\]

#### Step-by-Step Solution:
1. Solve the innermost parentheses:
\[
2 - 5 = -3
\]
So the expression becomes:
\[
[-9 - (-3)] \div (-6)
\]

2. Simplify the subtraction:
\[
-9 - (-3) = -9 + 3 = -6
\]
So the expression becomes:
\[
-6 \div (-6)
\]

3. Perform the division:
\[
-6 \div (-6) = 1
\]

#### Final Answer:
\[
\boxed{1}
\]

---

Problem 7:

\[
(-7 - 5) \div [2 - 2 - (-6)]
\]

#### Step-by-Step Solution:
1. Solve the numerator:
\[
-7 - 5 = -12
\]
So the expression becomes:
\[
-12 \div [2 - 2 - (-6)]
\]

2. Solve the denominator:
\[
2 - 2 - (-6) = 2 - 2 + 6 = 6
\]
So the expression becomes:
\[
-12 \div 6
\]

3. Perform the division:
\[
-12 \div 6 = -2
\]

#### Final Answer:
\[
\boxed{-2}
\]

---

Problem 8:

\[
[(36 \div 6) - (-1)^3]^2 + 11
\]

#### Step-by-Step Solution:
1. Solve the division inside the brackets:
\[
36 \div 6 = 6
\]
So the expression becomes:
\[
[6 - (-1)^3]^2 + 11
\]

2. Solve the exponent:
\[
(-1)^3 = -1
\]
So the expression becomes:
\[
[6 - (-1)]^2 + 11
\]

3. Simplify the subtraction:
\[
6 - (-1) = 6 + 1 = 7
\]
So the expression becomes:
\[
7^2 + 11
\]

4. Calculate the square:
\[
7^2 = 49
\]
So the expression becomes:
\[
49 + 11
\]

5. Perform the addition:
\[
49 + 11 = 60
\]

#### Final Answer:
\[
\boxed{60}
\]

---

Final Answers:

\[
\boxed{6, 2, 26, 0, -60, 1, -2, 60}
\]