To solve the expression \( 15 \div 2(4 + 74) \), we need to follow the order of operations (PEMDAS/BODMAS), which stands for:

1. **Parentheses/Brackets** 
2. **Exponents/Orders** 
3. **Multiplication and Division** (from left to right)
4. **Addition and Subtraction** (from left to right)

Let's break down the steps:

### Step 1: Solve the expression inside the parentheses.
\[
4 + 74 = 78
\]

### Step 2: Substitute back into the expression.
\[
15 \div 2(78)
\]

### Step 3: Understand the multiplication notation.
The expression \( 2(78) \) is equivalent to \( 2 \times 78 \). So, the expression becomes:
\[
15 \div 2 \times 78
\]

### Step 4: Perform the division and multiplication from left to right.
First, calculate:
\[
15 \div 2 = 7.5
\]

Then, multiply:
\[
7.5 \times 78 = 585
\]

### Final Answer:
\[
15 \div 2(4 + 74) = 585
\]

Would you like more details or have any questions?

Here are some related questions you might consider:

1. How does the order of operations affect calculations?
2. What happens if different operations are prioritized incorrectly?
3. Can parentheses change the result of a mathematical expression?
4. How do you handle expressions involving multiple operations and terms?
5. What are some common errors when performing calculations with mixed operations?

**Tip:** Always double-check the order of operations when solving mathematical expressions to avoid mistakes.

Learn how to solve the mathematical expression 15 ÷ 2(4 + 74) using the order of operations (PEMDAS/BODMAS). This problem covers understanding parentheses, multiplication, and division in mathematical expressions. Suitable for students in Grades 6-8.

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