This answer key breaks down ten order of operations problems step-by-step, showing exactly how to apply PEMDAS rules to reach the correct solution.

The worksheet provided involves solving mathematical expressions using the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Below is a detailed explanation of how each problem is solved step by step.

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Problem 1: \( 21 \div 3 + (3 \times 9) \times 9 + 5 \)

1. Step 1: Parentheses
\[
(3 \times 9) = 27
\]
Expression becomes:
\[
21 \div 3 + 27 \times 9 + 5
\]

2. Step 2: Multiplication and Division (from left to right)
- First, solve \( 21 \div 3 \):
\[
21 \div 3 = 7
\]
- Next, solve \( 27 \times 9 \):
\[
27 \times 9 = 243
\]
Expression becomes:
\[
7 + 243 + 5
\]

3. Step 3: Addition and Subtraction (from left to right)
- First, add \( 7 + 243 \):
\[
7 + 243 = 250
\]
- Next, add \( 250 + 5 \):
\[
250 + 5 = 255
\]

Final Answer:
\[
\boxed{255}
\]

---

Problem 2: \( 18 \div 6 \times (4 - 3) + 6 \)

1. Step 1: Parentheses
\[
(4 - 3) = 1
\]
Expression becomes:
\[
18 \div 6 \times 1 + 6
\]

2. Step 2: Multiplication and Division (from left to right)
- First, solve \( 18 \div 6 \):
\[
18 \div 6 = 3
\]
- Next, solve \( 3 \times 1 \):
\[
3 \times 1 = 3
\]
Expression becomes:
\[
3 + 6
\]

3. Step 3: Addition and Subtraction (from left to right)
- Add \( 3 + 6 \):
\[
3 + 6 = 9
\]

Final Answer:
\[
\boxed{9}
\]

---

Problem 3: \( 14 - 8 + 3 + 8 \times (24 \div 8) \)

1. Step 1: Parentheses
\[
(24 \div 8) = 3
\]
Expression becomes:
\[
14 - 8 + 3 + 8 \times 3
\]

2. Step 2: Multiplication and Division (from left to right)
- Solve \( 8 \times 3 \):
\[
8 \times 3 = 24
\]
Expression becomes:
\[
14 - 8 + 3 + 24
\]

3. Step 3: Addition and Subtraction (from left to right)
- First, subtract \( 14 - 8 \):
\[
14 - 8 = 6
\]
- Next, add \( 6 + 3 \):
\[
6 + 3 = 9
\]
- Finally, add \( 9 + 24 \):
\[
9 + 24 = 33
\]

Final Answer:
\[
\boxed{33}
\]

---

Problem 4: \( 4 \times 5 + (14 + 8) - 36 \div 9 \)

1. Step 1: Parentheses
\[
(14 + 8) = 22
\]
Expression becomes:
\[
4 \times 5 + 22 - 36 \div 9
\]

2. Step 2: Multiplication and Division (from left to right)
- Solve \( 4 \times 5 \):
\[
4 \times 5 = 20
\]
- Solve \( 36 \div 9 \):
\[
36 \div 9 = 4
\]
Expression becomes:
\[
20 + 22 - 4
\]

3. Step 3: Addition and Subtraction (from left to right)
- First, add \( 20 + 22 \):
\[
20 + 22 = 42
\]
- Next, subtract \( 42 - 4 \):
\[
42 - 4 = 38
\]

Final Answer:
\[
\boxed{38}
\]

---

Problem 5: \( (17 - 7) \times 6 + 2 + 56 - 8 \)

1. Step 1: Parentheses
\[
(17 - 7) = 10
\]
Expression becomes:
\[
10 \times 6 + 2 + 56 - 8
\]

2. Step 2: Multiplication and Division (from left to right)
- Solve \( 10 \times 6 \):
\[
10 \times 6 = 60
\]
Expression becomes:
\[
60 + 2 + 56 - 8
\]

3. Step 3: Addition and Subtraction (from left to right)
- First, add \( 60 + 2 \):
\[
60 + 2 = 62
\]
- Next, add \( 62 + 56 \):
\[
62 + 56 = 118
\]
- Finally, subtract \( 118 - 8 \):
\[
118 - 8 = 110
\]

Final Answer:
\[
\boxed{110}
\]

---

Problem 6: \( (28 \div 4) + 3 + (10 - 8) \times 5 \)

1. Step 1: Parentheses
- Solve \( 28 \div 4 \):
\[
28 \div 4 = 7
\]
- Solve \( 10 - 8 \):
\[
10 - 8 = 2
\]
Expression becomes:
\[
7 + 3 + 2 \times 5
\]

2. Step 2: Multiplication and Division (from left to right)
- Solve \( 2 \times 5 \):
\[
2 \times 5 = 10
\]
Expression becomes:
\[
7 + 3 + 10
\]

3. Step 3: Addition and Subtraction (from left to right)
- First, add \( 7 + 3 \):
\[
7 + 3 = 10
\]
- Next, add \( 10 + 10 \):
\[
10 + 10 = 20
\]

Final Answer:
\[
\boxed{20}
\]

---

Problem 7: \( 12 - 5 + 6 \times 3 + 20 \div 4 \)

1. Step 1: Multiplication and Division (from left to right)
- Solve \( 6 \times 3 \):
\[
6 \times 3 = 18
\]
- Solve \( 20 \div 4 \):
\[
20 \div 4 = 5
\]
Expression becomes:
\[
12 - 5 + 18 + 5
\]

2. Step 2: Addition and Subtraction (from left to right)
- First, subtract \( 12 - 5 \):
\[
12 - 5 = 7
\]
- Next, add \( 7 + 18 \):
\[
7 + 18 = 25
\]
- Finally, add \( 25 + 5 \):
\[
25 + 5 = 30
\]

Final Answer:
\[
\boxed{30}
\]

---

Problem 8: \( 36 \div 9 + 48 - 10 \div 2 \)

1. Step 1: Multiplication and Division (from left to right)
- Solve \( 36 \div 9 \):
\[
36 \div 9 = 4
\]
- Solve \( 10 \div 2 \):
\[
10 \div 2 = 5
\]
Expression becomes:
\[
4 + 48 - 5
\]

2. Step 2: Addition and Subtraction (from left to right)
- First, add \( 4 + 48 \):
\[
4 + 48 = 52
\]
- Next, subtract \( 52 - 5 \):
\[
52 - 5 = 47
\]

Final Answer:
\[
\boxed{47}
\]

---

Problem 9: \( 10 + 8 \times 90 \div 9 - 4 \)

1. Step 1: Multiplication and Division (from left to right)
- Solve \( 8 \times 90 \):
\[
8 \times 90 = 720
\]
- Solve \( 720 \div 9 \):
\[
720 \div 9 = 80
\]
Expression becomes:
\[
10 + 80 - 4
\]

2. Step 2: Addition and Subtraction (from left to right)
- First, add \( 10 + 80 \):
\[
10 + 80 = 90
\]
- Next, subtract \( 90 - 4 \):
\[
90 - 4 = 86
\]

Final Answer:
\[
\boxed{86}
\]

---

Problem 10: \( 8 \times 3 + 70 \div 7 - 7 \)

1. Step 1: Multiplication and Division (from left to right)
- Solve \( 8 \times 3 \):
\[
8 \times 3 = 24
\]
- Solve \( 70 \div 7 \):
\[
70 \div 7 = 10
\]
Expression becomes:
\[
24 + 10 - 7
\]

2. Step 2: Addition and Subtraction (from left to right)
- First, add \( 24 + 10 \):
\[
24 + 10 = 34
\]
- Next, subtract \( 34 - 7 \):
\[
34 - 7 = 27
\]

Final Answer:
\[
\boxed{27}
\]

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Final Answer Key:

\[
\boxed{255, 9, 33, 38, 110, 20, 30, 47, 86, 27}
\]