The problem asks us to first rewrite the given expression $\frac{(3.65 + 5.49) \times 9.84}{5.16 \times (12.1 - 8.52)}$ by rounding each number to the nearest whole number. Then, we are asked to estimate the value of the original expression using the rewritten expression, rounding the final result to the nearest whole number.

1. Problem Description

The problem asks us to first rewrite the given expression $\frac{(3.65 + 5.49) \times 9.84}{5.16 \times (12.1 - 8.52)}$ by rounding each number to the nearest whole number. Then, we are asked to estimate the value of the original expression using the rewritten expression, rounding the final result to the nearest whole number.

2. Solution Steps

First, we round each number to the nearest whole number:

$3.65 \approx 4$

$5.49 \approx 5$

$9.84 \approx 10$

$5.16 \approx 5$

$12.1 \approx 12$

$8.52 \approx 9$

So the rewritten expression is:

$\frac{(4 + 5) \times 10}{5 \times (12 - 9)}$

Now we simplify the expression:

$\frac{(4 + 5) \times 10}{5 \times (12 - 9)} = \frac{9 \times 10}{5 \times 3} = \frac{90}{15} = 6$

3. Final Answer

The estimated value of the expression, rounded to the nearest whole number, is 6.