What approximate value should come in place of the question mark (?) in the following questions ? (You are not expected to calculate the exact value) ?
`(4)/(5) xx (1225)/(1428) xx 9 = ?`

Options

A. 6
B. 8
C. 9
D. 3

Answer

To solve the problem \( \frac{4}{5} \times \frac{1225}{1428} \times 9 = ? \), we can follow these steps:

### Step 1: Simplify the fractions
We start with the expression:
\[ \frac{4}{5} \times \frac{1225}{1428} \times 9 \]

### Step 2: Estimate the fractions
Instead of calculating the exact values, we can estimate:
- \( \frac{4}{5} \) is approximately \( 0.8 \).
- For \( \frac{1225}{1428} \), we can simplify it:
- \( 1225 \) is close to \( 1200 \) and \( 1428 \) is close to \( 1400 \).
- Therefore, \( \frac{1225}{1428} \approx \frac{1200}{1400} = \frac{12}{14} = \frac{6}{7} \approx 0.857 \).

### Step 3: Multiply the approximations
Now we can multiply the approximated values:
\[ 0.8 \times 0.857 \approx 0.6856 \]

### Step 4: Multiply by 9
Next, we multiply this result by \( 9 \):
\[ 0.6856 \times 9 \approx 6.1 \]

### Step 5: Round to the nearest whole number
The approximate value is \( 6.1 \), which we can round to \( 6 \).

### Final Answer
Thus, the approximate value that should come in place of the question mark (?) is:
\[ \boxed{6} \]