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.