Which one of the following of the best approximation of `(7.1xx3.85)/(9.09)`?

Options

A. `(7xx3)/(10)`
B. `(7xx3)/9`
C. `(7xx4)/9`
D. `(7xx4)/(10)`

Answer

To solve the problem of finding the best approximation for \((7.1 \times 3.85) / 9.09\), we will follow these steps:

### Step 1: Approximate the numbers
We will round each number to make the calculation simpler.

- **For 7.1**: Since the decimal part (0.1) is less than 0.5, we round down to **7**.
- **For 3.85**: The decimal part (0.85) is greater than 0.5, so we round up to **4**.
- **For 9.09**: The decimal part (0.09) is less than 0.5, so we round down to **9**.

### Step 2: Substitute the approximated values
Now we substitute the approximated values into the expression:

\[ \frac{7 \times 4}{9} \]

### Step 3: Calculate the expression
Now we calculate the expression:

\[ 7 \times 4 = 28 \]

So, we have:

\[ \frac{28}{9} \]

### Step 4: Simplify the fraction
To simplify \(\frac{28}{9}\), we can leave it as it is or convert it to a decimal if necessary. However, since we are looking for an approximation, we can also leave it in this form.

### Conclusion
The best approximation of \((7.1 \times 3.85) / 9.09\) is:

\[ \frac{7 \times 4}{9} \]

Thus, the correct option is **C: \( \frac{7 \times 4}{9} \)**.

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