In the following question, correct the equation 8 × 3 ÷ 4 + 9 − 5 = 16 by interchanging two numbers. Which pair of numbers must be swapped?

Introduction / Context:
This problem presents a numerical equation that is currently incorrect under normal arithmetic rules. You are allowed to fix it by interchanging (swapping) two numbers. The challenge is to determine which pair of numbers must be swapped so that the left-hand side evaluates exactly to the right-hand side when standard rules of arithmetic are applied.

Given Data / Assumptions:

- Original equation: 8 × 3 ÷ 4 + 9 − 5 = 16.
- Candidate pairs to swap: (3,4), (4,8), (5,3), (5,9).
- Only two numbers are to be swapped, and all operators stay as they are.
- Standard precedence rules apply: multiplication and division before addition and subtraction.

Concept / Approach:
First, evaluate the original left-hand side to confirm that the equation is indeed incorrect. Then, for each possible pair from the options, swap the two numbers in the expression and recalculate the left-hand side. The correct pair is the one that produces 16. Because there are only four options, a direct trial is simple and reliable.

Step-by-Step Solution:
Step 1: Evaluate the original left-hand side. Expression: 8 × 3 ÷ 4 + 9 − 5. Compute 8 × 3 = 24. Compute 24 ÷ 4 = 6. Then 6 + 9 = 15. 15 − 5 = 10. Thus LHS = 10, which is not 16. Step 2: Test swapping 5 and 3 (option C). After swapping 5 and 3, the expression becomes 8 × 5 ÷ 4 + 9 − 3. Now evaluate step by step: 8 × 5 = 40. 40 ÷ 4 = 10. 10 + 9 = 19. 19 − 3 = 16. Now LHS = 16, which matches the right-hand side.

Verification / Alternative check:
We can quickly verify that other swaps do not work. Swapping 3 and 4, or 4 and 8, or 5 and 9 each leads to a new expression whose value is not 16 when evaluated correctly. Hence, option C is the only pair that fixes the equation.

Why Other Options Are Wrong:

- Swapping 3 and 4 leads to 8 × 4 ÷ 3 + 9 − 5, which does not evaluate to 16.
- Swapping 4 and 8 gives 4 × 3 ÷ 8 + 9 − 5, whose value is also not 16.
- Swapping 5 and 9 yields 8 × 3 ÷ 4 + 5 − 9, a much smaller result.

Only swapping 5 and 3 produces the required value of 16.

Common Pitfalls:
Students sometimes swap the numbers but forget to recompute with correct precedence, or they might mistakenly swap more than two numbers. Another error is to try to swap operators instead of numbers, which is not allowed in this question. Careful, methodical testing of each candidate pair avoids these issues.

Final Answer:
The equation is corrected by interchanging the numbers 5 and 3. Therefore, the correct pair to swap is 5 and 3.