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Let's solve these sums one by one using the **BODMAS** rule. BODMAS stands for Brackets, Orders (powers and square roots, etc.), Division, Multiplication, Addition, and Subtraction, and it dictates the order of operations.

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### 1. \( 3 \times 3 + (26 \times 4) + 19 + 27 \)

- \( 3 \times 3 = 9 \)
- \( 26 \times 4 = 104 \)
- Now, \( 9 + 104 + 19 + 27 = 159 \)

So, the answer is **159**.

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### 2. \( 2 + 23 + 28 \times 3 - (18 + 29) \)

- \( 28 \times 3 = 84 \)
- \( 18 + 29 = 47 \)
- Now, \( 2 + 23 + 84 - 47 = 62 \)

So, the answer is **62**.

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### 3. \( 20 + 40 + (20 \times 10) \times 5 \times 5 \)

- \( 20 \times 10 = 200 \)
- \( 200 \times 5 = 1000 \)
- \( 1000 \times 5 = 5000 \)
- Now, \( 20 + 40 + 5000 = 5060 \)

So, the answer is **5060**.

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### 4. \( 29 - 15 + 3 + (31 \times 2 + 28) \)

- \( 31 \times 2 = 62 \)
- \( 62 + 28 = 90 \)
- Now, \( 29 - 15 + 3 + 90 = 107 \)

So, the answer is **107**.

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### 5. \( 1 \times 2 \times 6 \times (7 + 19 + 21) \)

- \( 7 + 19 + 21 = 47 \)
- \( 1 \times 2 \times 6 = 12 \)
- Now, \( 12 \times 47 = 564 \)

So, the answer is **564**.

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If you want, I can continue with the remaining problems. Would you like me to? Also, here are 5 follow-up questions related to these concepts:

1. How does BODMAS apply when there are nested brackets?
2. What is the difference between BODMAS and PEMDAS?
3. How does the BODMAS rule handle exponents and roots?
4. What happens if addition and subtraction are inside the same bracket?
5. Why is it important to follow BODMAS for correct results in multi-step calculations?

**Tip:** Always solve the operations inside the brackets first to ensure that your order of operations is correct!

Solve a set of arithmetic problems using the BODMAS rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction). Includes step-by-step solutions for problems suitable for Grades 6-8.

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