Evaluate a sum of three rational subexpressions Compute: (20 ÷ 5) ÷ 2 + (16 ÷ 8) * 2 + (10 ÷ 5) * (3 ÷ 2).

Introduction / Context:
This computation combines nested divisions and multiplications. Breaking each parenthesized term into a simple number first keeps the process clean and avoids left-to-right precedence mistakes inside the groups.

Given Data / Assumptions:

• Expression: (20 ÷ 5) ÷ 2 + (16 ÷ 8) * 2 + (10 ÷ 5) * (3 ÷ 2).
• Parentheses isolate each mini-calculation.
• No rounding; all results are exact.

Concept / Approach:
Evaluate the three grouped parts individually, then add. Each part simplifies to an integer or a simple fraction: this reduces error and makes mental arithmetic easy.

Step-by-Step Solution:
Part 1: (20 ÷ 5) ÷ 2 = 4 ÷ 2 = 2.Part 2: (16 ÷ 8) * 2 = 2 * 2 = 4.Part 3: (10 ÷ 5) * (3 ÷ 2) = 2 * 3/2 = 3.Sum: 2 + 4 + 3 = 9.

Verification / Alternative check:
Fraction approach: (20/5)/2 = 4/2 = 2; (16/8)*2 = 2*2 = 4; (10/5)*(3/2) = 2*(3/2) = 3. Totals to 9 again, confirming consistency.

Why Other Options Are Wrong:
12, 15, 18 result from incorrectly doubling one term or miscomputing 3/2 as 1 or 2.

Common Pitfalls:
Dropping parentheses and applying left-to-right globally; misreading 3 ÷ 2 as 2 ÷ 3; or assuming every part must be an integer before summing.

Final Answer:
9