Estimate to the closest integer: What is `(11)/(40)" of "(5)/(16)" of "120`?

Answer

To solve the problem step by step, we need to calculate \( \frac{11}{40} \) of \( \frac{5}{16} \) of \( 120 \).

### Step 1: Calculate \( \frac{5}{16} \) of \( 120 \)

To find \( \frac{5}{16} \) of \( 120 \), we multiply \( 120 \) by \( \frac{5}{16} \):

\[ \frac{5}{16} \times 120 = \frac{5 \times 120}{16} \]

Calculating \( 5 \times 120 \):

\[ 5 \times 120 = 600 \]

Now, divide \( 600 \) by \( 16 \):

\[ \frac{600}{16} = 37.5 \]

### Step 2: Calculate \( \frac{11}{40} \) of \( 37.5 \)

Next, we need to find \( \frac{11}{40} \) of \( 37.5 \):

\[ \frac{11}{40} \times 37.5 = \frac{11 \times 37.5}{40} \]

Calculating \( 11 \times 37.5 \):

\[ 11 \times 37.5 = 412.5 \]

Now, divide \( 412.5 \) by \( 40 \):

\[ \frac{412.5}{40} = 10.3125 \]

### Step 3: Round to the closest integer

Now, we round \( 10.3125 \) to the closest integer. The closest integer to \( 10.3125 \) is \( 10 \).

### Final Answer

Thus, the final answer is:

\[ \boxed{10} \]