Math worksheet practicing order of operations (PEMDAS) with various arithmetic expressions.

To solve these problems, we will use the order of operations (PEMDAS), which stands for:

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

Let's solve each problem step by step.

---

1. \( 10 + 5 \times (9 - 4) \)

- Step 1: Solve the expression inside the parentheses.
\[
9 - 4 = 5
\]
So the expression becomes:
\[
10 + 5 \times 5
\]

- Step 2: Perform multiplication.
\[
5 \times 5 = 25
\]
So the expression becomes:
\[
10 + 25
\]

- Step 3: Perform addition.
\[
10 + 25 = 35
\]

Answer: \( \boxed{35} \)

---

2. \( (9 - 6 + 5) \div 2 \)

- Step 1: Solve the expression inside the parentheses.
\[
9 - 6 + 5 = 3 + 5 = 8
\]
So the expression becomes:
\[
8 \div 2
\]

- Step 2: Perform division.
\[
8 \div 2 = 4
\]

Answer: \( \boxed{4} \)

---

3. \( (8 + 3 - 6) \div 5 \)

- Step 1: Solve the expression inside the parentheses.
\[
8 + 3 - 6 = 11 - 6 = 5
\]
So the expression becomes:
\[
5 \div 5
\]

- Step 2: Perform division.
\[
5 \div 5 = 1
\]

Answer: \( \boxed{1} \)

---

4. \( 10 \times 7 + 3 - 4 \)

- Step 1: Perform multiplication.
\[
10 \times 7 = 70
\]
So the expression becomes:
\[
70 + 3 - 4
\]

- Step 2: Perform addition and subtraction from left to right.
\[
70 + 3 = 73
\]
\[
73 - 4 = 69
\]

Answer: \( \boxed{69} \)

---

5. \( 10 \times (6 + 3) \div 2 \)

- Step 1: Solve the expression inside the parentheses.
\[
6 + 3 = 9
\]
So the expression becomes:
\[
10 \times 9 \div 2
\]

- Step 2: Perform multiplication.
\[
10 \times 9 = 90
\]
So the expression becomes:
\[
90 \div 2
\]

- Step 3: Perform division.
\[
90 \div 2 = 45
\]

Answer: \( \boxed{45} \)

---

6. \( 8 \times 2 + 5 - 6 \)

- Step 1: Perform multiplication.
\[
8 \times 2 = 16
\]
So the expression becomes:
\[
16 + 5 - 6
\]

- Step 2: Perform addition and subtraction from left to right.
\[
16 + 5 = 21
\]
\[
21 - 6 = 15
\]

Answer: \( \boxed{15} \)

---

7. \( 8 + 7 \times (4 - 3) \)

- Step 1: Solve the expression inside the parentheses.
\[
4 - 3 = 1
\]
So the expression becomes:
\[
8 + 7 \times 1
\]

- Step 2: Perform multiplication.
\[
7 \times 1 = 7
\]
So the expression becomes:
\[
8 + 7
\]

- Step 3: Perform addition.
\[
8 + 7 = 15
\]

Answer: \( \boxed{15} \)

---

8. \( 6 + 3 - 4 \div 2 \)

- Step 1: Perform division.
\[
4 \div 2 = 2
\]
So the expression becomes:
\[
6 + 3 - 2
\]

- Step 2: Perform addition and subtraction from left to right.
\[
6 + 3 = 9
\]
\[
9 - 2 = 7
\]

Answer: \( \boxed{7} \)

---

9. \( 8 \times 5 - 4 + 7 \)

- Step 1: Perform multiplication.
\[
8 \times 5 = 40
\]
So the expression becomes:
\[
40 - 4 + 7
\]

- Step 2: Perform subtraction and addition from left to right.
\[
40 - 4 = 36
\]
\[
36 + 7 = 43
\]

Answer: \( \boxed{43} \)

---

10. \( 4 \times 6 \div (10 + 2) \)

- Step 1: Solve the expression inside the parentheses.
\[
10 + 2 = 12
\]
So the expression becomes:
\[
4 \times 6 \div 12
\]

- Step 2: Perform multiplication.
\[
4 \times 6 = 24
\]
So the expression becomes:
\[
24 \div 12
\]

- Step 3: Perform division.
\[
24 \div 12 = 2
\]

Answer: \( \boxed{2} \)

---

Final Answers:

\[
\boxed{35, 4, 1, 69, 45, 15, 15, 7, 43, 2}
\]