PEMDAS Rule Worksheet featuring 10 mathematical expressions to solve using the order of operations.

To solve the given problems using the PEMDAS rule (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), let's evaluate each expression step by step.

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Problem 1: \( 35 \div 7 + 2^2 \)

1. Exponents: \( 2^2 = 4 \)
\[
35 \div 7 + 2^2 = 35 \div 7 + 4
\]

2. Division: \( 35 \div 7 = 5 \)
\[
35 \div 7 + 4 = 5 + 4
\]

3. Addition: \( 5 + 4 = 9 \)

Answer: \( \boxed{9} \)

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Problem 2: \( 2.5 \times (13 - 5) \)

1. Parentheses: \( 13 - 5 = 8 \)
\[
2.5 \times (13 - 5) = 2.5 \times 8
\]

2. Multiplication: \( 2.5 \times 8 = 20 \)

Answer: \( \boxed{20} \)

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Problem 3: \( 45 \div (6 + 3) \times 3 - 6 \div 2 \)

1. Parentheses: \( 6 + 3 = 9 \)
\[
45 \div (6 + 3) \times 3 - 6 \div 2 = 45 \div 9 \times 3 - 6 \div 2
\]

2. Division: \( 45 \div 9 = 5 \) and \( 6 \div 2 = 3 \)
\[
45 \div 9 \times 3 - 6 \div 2 = 5 \times 3 - 3
\]

3. Multiplication: \( 5 \times 3 = 15 \)
\[
5 \times 3 - 3 = 15 - 3
\]

4. Subtraction: \( 15 - 3 = 12 \)

Answer: \( \boxed{12} \)

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Problem 4: \( 48 - 3(16 + 15 \div 5 \times 3 - 2 \times 3) + 8 \)

1. Parentheses: Solve inside the parentheses first.
- Division: \( 15 \div 5 = 3 \)
\[
16 + 15 \div 5 \times 3 - 2 \times 3 = 16 + 3 \times 3 - 2 \times 3
\]
- Multiplication: \( 3 \times 3 = 9 \) and \( 2 \times 3 = 6 \)
\[
16 + 3 \times 3 - 2 \times 3 = 16 + 9 - 6
\]
- Addition and Subtraction: \( 16 + 9 - 6 = 19 \)
\[
16 + 15 \div 5 \times 3 - 2 \times 3 = 19
\]

2. Multiplication: \( 3 \times 19 = 57 \)
\[
48 - 3(16 + 15 \div 5 \times 3 - 2 \times 3) + 8 = 48 - 57 + 8
\]

3. Subtraction and Addition: \( 48 - 57 = -9 \) and \( -9 + 8 = -1 \)
\[
48 - 57 + 8 = -1
\]

Answer: \( \boxed{-1} \)

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Problem 5: \( 7 + [(25 - 1) \div (3^2 - 3)] - 3 \)

1. Parentheses: Solve inside the parentheses first.
- \( 25 - 1 = 24 \)
- Exponents: \( 3^2 = 9 \)
\[
3^2 - 3 = 9 - 3 = 6
\]
- Division: \( (25 - 1) \div (3^2 - 3) = 24 \div 6 = 4 \)
\[
[(25 - 1) \div (3^2 - 3)] = 4
\]

2. Addition and Subtraction: \( 7 + 4 - 3 \)
\[
7 + 4 - 3 = 11 - 3 = 8
\]

Answer: \( \boxed{8} \)

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Problem 6: \( (63 \div 7) + 22 \times (9 + 1) \div 11 \)

1. Parentheses: Solve inside the parentheses first.
- \( 63 \div 7 = 9 \)
- \( 9 + 1 = 10 \)
\[
(63 \div 7) + 22 \times (9 + 1) \div 11 = 9 + 22 \times 10 \div 11
\]

2. Multiplication and Division: Perform multiplication and division from left to right.
- \( 22 \times 10 = 220 \)
- \( 220 \div 11 = 20 \)
\[
9 + 22 \times 10 \div 11 = 9 + 20
\]

3. Addition: \( 9 + 20 = 29 \)

Answer: \( \boxed{29} \)

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Problem 7: \( (146 - 2) \div (3 \times 4) - 15 + 9 \)

1. Parentheses: Solve inside the parentheses first.
- \( 146 - 2 = 144 \)
- \( 3 \times 4 = 12 \)
\[
(146 - 2) \div (3 \times 4) - 15 + 9 = 144 \div 12 - 15 + 9
\]

2. Division: \( 144 \div 12 = 12 \)
\[
144 \div 12 - 15 + 9 = 12 - 15 + 9
\]

3. Subtraction and Addition: \( 12 - 15 = -3 \) and \( -3 + 9 = 6 \)
\[
12 - 15 + 9 = 6
\]

Answer: \( \boxed{6} \)

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Problem 8: \( 78 \div 13 + (24 - 12) \times 5 \)

1. Parentheses: Solve inside the parentheses first.
- \( 24 - 12 = 12 \)
\[
78 \div 13 + (24 - 12) \times 5 = 78 \div 13 + 12 \times 5
\]

2. Division and Multiplication: Perform division and multiplication from left to right.
- \( 78 \div 13 = 6 \)
- \( 12 \times 5 = 60 \)
\[
78 \div 13 + 12 \times 5 = 6 + 60
\]

3. Addition: \( 6 + 60 = 66 \)

Answer: \( \boxed{66} \)

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Problem 9: \( (24 + 1) \times 2 \div (13 - 3) - 19 \)

1. Parentheses: Solve inside the parentheses first.
- \( 24 + 1 = 25 \)
- \( 13 - 3 = 10 \)
\[
(24 + 1) \times 2 \div (13 - 3) - 19 = 25 \times 2 \div 10 - 19
\]

2. Multiplication and Division: Perform multiplication and division from left to right.
- \( 25 \times 2 = 50 \)
- \( 50 \div 10 = 5 \)
\[
25 \times 2 \div 10 - 19 = 5 - 19
\]

3. Subtraction: \( 5 - 19 = -14 \)

Answer: \( \boxed{-14} \)

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Problem 10: \( [12 - 36 \div (4^2 - 4) \div 3 + 2] \times 5 \)

1. Parentheses: Solve inside the parentheses first.
- Exponents: \( 4^2 = 16 \)
\[
4^2 - 4 = 16 - 4 = 12
\]
- Division: \( 36 \div 12 = 3 \)
\[
36 \div (4^2 - 4) = 36 \div 12 = 3
\]
- Further Division: \( 3 \div 3 = 1 \)
\[
36 \div (4^2 - 4) \div 3 = 3 \div 3 = 1
\]
- Subtraction and Addition: \( 12 - 1 + 2 = 11 + 2 = 13 \)
\[
[12 - 36 \div (4^2 - 4) \div 3 + 2] = 13
\]

2. Multiplication: \( 13 \times 5 = 65 \)

Answer: \( \boxed{65} \)

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Final Answers:

1. \( \boxed{9} \)
2. \( \boxed{20} \)
3. \( \boxed{12} \)
4. \( \boxed{-1} \)
5. \( \boxed{8} \)
6. \( \boxed{29} \)
7. \( \boxed{6} \)
8. \( \boxed{66} \)
9. \( \boxed{-14} \)
10. \( \boxed{65} \)