Order of Operations practice worksheet with answers and working out for each problem.

The task involves solving a series of mathematical expressions using the order of operations (PEMDAS/BODMAS rules). Let's go through each expression step by step to ensure the solutions are correct.

Order of Operations Recap:

1. Parentheses/Brackets (`()` or `[]`)
2. Exponents/Orders (Powers and Square Roots, etc.)
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

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Solutions:

#### 1. \( 4 + 7 \times 3 - 6 \)
- Working Out:
\( = 4 + 21 - 6 \)
\( = 25 - 6 \)
\( = 19 \)
- Answer: \( 19 \)

#### 2. \( (7 + 11) \div 3 - 5 \)
- Working Out:
\( = 18 \div 3 - 5 \)
\( = 6 - 5 \)
\( = 1 \)
- Answer: \( 1 \)

#### 3. \( 9 \times (8 - 5) + 6 \)
- Working Out:
\( = 9 \times 3 + 6 \)
\( = 27 + 6 \)
\( = 33 \)
- Answer: \( 33 \)

#### 4. \( 6 - 2 \times 5 + 8 \)
- Working Out:
\( = 6 - 10 + 8 \)
\( = -4 + 8 \)
\( = 4 \)
- Answer: \( 4 \)

#### 5. \( 8 \times 5 \div 4 - 9 \)
- Working Out:
\( = 40 \div 4 - 9 \)
\( = 10 - 9 \)
\( = 1 \)
- Answer: \( 1 \)

#### 6. \( 4 - 7 \times (5 - 3) + 6 \)
- Working Out:
\( = 4 - 7 \times 2 + 6 \)
\( = 4 - 14 + 6 \)
\( = -10 + 6 \)
\( = -4 \)
- Answer: \( -4 \)

#### 7. \( 30 - (10 - 8) \times (4 + 3) \)
- Working Out:
\( = 30 - 2 \times 7 \)
\( = 30 - 14 \)
\( = 16 \)
- Answer: \( 16 \)

#### 8. \( 4 \times 8 - 7 \times 6 \)
- Working Out:
\( = 32 - 42 \)
\( = -10 \)
- Answer: \( -10 \)

#### 9. \( \frac{1}{2} \times (12 + 6) - 4 \)
- Working Out:
\( = \frac{1}{2} \times 18 - 4 \)
\( = 9 - 4 \)
\( = 5 \)
- Answer: \( 5 \)

#### 10. \( 8 \times \left( \frac{3}{4} + \frac{1}{4} \right) - 5 \)
- Working Out:
\( = 8 \times 1 - 5 \)
\( = 8 - 5 \)
\( = 3 \)
- Answer: \( 3 \)

#### 11. \( (5 + 4)^2 \)
- Working Out:
\( = 9^2 \)
\( = 81 \)
- Answer: \( 81 \)

#### 12. \( 5^2 - (3 + 2)^2 \)
- Working Out:
\( = 25 - 5^2 \)
\( = 25 - 25 \)
\( = 0 \)
- Answer: \( 0 \)

#### 13. \( \frac{1}{2} \times (23 - 9) + \frac{1}{4} \times (15 - 7) \)
- Working Out:
\( = \frac{1}{2} \times 14 + \frac{1}{4} \times 8 \)
\( = 7 + 2 \)
\( = 9 \)
- Answer: \( 9 \)

#### 14. \( 18 \div (2^2 + 5) \)
- Working Out:
\( = 18 \div (4 + 5) \)
\( = 18 \div 9 \)
\( = 2 \)
- Answer: \( 2 \)

#### 15. \( (6^2 + 12) \div (3^2 - 1) \)
- Working Out:
\( = (36 + 12) \div (9 - 1) \)
\( = 48 \div 8 \)
\( = 6 \)
- Answer: \( 6 \)

#### 16. \( \frac{3}{4} \times (5 + 12 \div 4) \)
- Working Out:
\( = \frac{3}{4} \times (5 + 3) \)
\( = \frac{3}{4} \times 8 \)
\( = 6 \)
- Answer: \( 6 \)

#### 17. \( (3^2 - 7) \times (2^2 + 8) \)
- Working Out:
\( = (9 - 7) \times (4 + 8) \)
\( = 2 \times 12 \)
\( = 24 \)
- Answer: \( 24 \)

#### 18. \( 7 \times 5 - 4 \times 6 + 3 \times 9 \)
- Working Out:
\( = 35 - 24 + 27 \)
\( = 11 + 27 \)
\( = 38 \)
- Answer: \( 38 \)

#### 19. \( 7 \times 4 \div 2 + 5 \times 3 \)
- Working Out:
\( = 28 \div 2 + 15 \)
\( = 14 + 15 \)
\( = 29 \)
- Answer: \( 29 \)

#### 20. \( (5^2 - 7) \div (4^2 + 2) \)
- Working Out:
\( = (25 - 7) \div (16 + 2) \)
\( = 18 \div 18 \)
\( = 1 \)
- Answer: \( 1 \)

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Final Answer:

\[
\boxed{19, 1, 33, 4, 1, -4, 16, -10, 5, 3, 81, 0, 9, 2, 6, 6, 24, 38, 29, 1}
\]