36. Brace bracket parentheses 7+5 parentheses divided by 6×9 bracket +24.

To solve the expression:

\[
36 \{ (7 + 5) \div (6 \times 9) \} + 24
\]

We'll follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

### Step 1: Solve inside the parentheses

\[
7 + 5 = 12
\]

Now the expression becomes:

\[
36 \{ 12 \div (6 \times 9) \} + 24
\]

### Step 2: Multiply inside the second parentheses

\[
6 \times 9 = 54
\]

Now the expression becomes:

\[
36 \{ 12 \div 54 \} + 24
\]

### Step 3: Divide inside the braces

\[
12 \div 54 = \frac{12}{54} = \frac{2}{9}
\]

Now the expression becomes:

\[
36 \times \frac{2}{9} + 24
\]

### Step 4: Multiply

\[
36 \times \frac{2}{9} = 8
\]

Now the expression becomes:

\[
8 + 24
\]

### Step 5: Add

\[
8 + 24 = 32
\]

### Final Answer:
\[
\boxed{32}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you solve more complex expressions with nested parentheses?
2. What are the rules for operations involving fractions in expressions?
3. How does the order of operations work with both multiplication and division?
4. Can parentheses affect the outcome in expressions involving exponents?
5. What are some real-life applications of order of operations?

**Tip:** Always solve the innermost parentheses first when dealing with complex expressions.

Learn how to solve the arithmetic expression 36{(7 + 5) ÷ (6 × 9)} + 24 step-by-step using the order of operations (PEMDAS). This solution covers key concepts in arithmetic and fractions, suitable for students in Grades 6-8.

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