Solve the ff expressions
1. 12 - 3 + 8 ÷ (6 x 3) =

2. 7 x 9 - (3 + 8) =

3. 18 - 12 ÷ 6 + 7 =

4. 9 x (9 ÷ 3) - 9 + 6 =

5. 16 ÷ 4 x 5 - 7 + 8

Let's solve each of these expressions step by step:

### 1. \( 12 - 3 + \frac{8}{6 \times 3} \)
- First, calculate the multiplication in the denominator: \( 6 \times 3 = 18 \).
- Now, divide: \( \frac{8}{18} \). Simplify to \( \frac{4}{9} \).
- The expression becomes \( 12 - 3 + \frac{4}{9} \).
- Subtract: \( 12 - 3 = 9 \).
- Finally, add the fraction: \( 9 + \frac{4}{9} = \frac{81}{9} + \frac{4}{9} = \frac{85}{9} \).

The result is \( \frac{85}{9} \) or approximately \( 9.44 \).

### 2. \( 7 \times 9 - (3 + 8) \)
- First, solve inside the parentheses: \( 3 + 8 = 11 \).
- Then, multiply: \( 7 \times 9 = 63 \).
- Finally, subtract: \( 63 - 11 = 52 \).

The result is \( 52 \).

### 3. \( 18 - \frac{12}{6} + 7 \)
- First, divide: \( \frac{12}{6} = 2 \).
- The expression becomes \( 18 - 2 + 7 \).
- Subtract: \( 18 - 2 = 16 \).
- Finally, add: \( 16 + 7 = 23 \).

The result is \( 23 \).

### 4. \( 9 \times \left(\frac{9}{3}\right) - 9 + 6 \)
- First, divide inside the parentheses: \( \frac{9}{3} = 3 \).
- The expression becomes \( 9 \times 3 - 9 + 6 \).
- Multiply: \( 9 \times 3 = 27 \).
- Then subtract: \( 27 - 9 = 18 \).
- Finally, add: \( 18 + 6 = 24 \).

The result is \( 24 \).

### 5. \( \frac{16}{4} \times 5 - 7 + 8 \)
- First, divide: \( \frac{16}{4} = 4 \).
- The expression becomes \( 4 \times 5 - 7 + 8 \).
- Multiply: \( 4 \times 5 = 20 \).
- Then subtract: \( 20 - 7 = 13 \).
- Finally, add: \( 13 + 8 = 21 \).

The result is \( 21 \).

### Final Answers:
1. \( \frac{85}{9} \) or approximately \( 9.44 \)
2. \( 52 \)
3. \( 23 \)
4. \( 24 \)
5. \( 21 \)

Do you want details on any specific step or have any questions?

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Here are some related questions to further your understanding:
1. How does the order of operations affect the result?
2. What happens if we change the operation sequence in one of these problems?
3. Can you simplify fractions like \( \frac{85}{9} \) in other ways?
4. How does using parentheses change the result of an expression?
5. What if the division in problem 3 was reversed, as \( 6 \div 12 \)?
6. How do you handle expressions with multiple parentheses?
7. What are common mistakes in solving such expressions?
8. How would you solve a similar expression involving exponents?

**Tip:** Always follow the order of operations (PEMDAS/BODMAS) to get the correct result in mathematical expressions.

Learn how to solve arithmetic expressions step-by-step with detailed explanations and solutions. This problem set covers various arithmetic operations including addition, subtraction, multiplication, division, and fractions. Suitable for students in Grades 6-8.

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