What approximate value should come in place of question mark (?) in the following questions ? (Note: You are not expected to calculate the exact value)
`5(7)/(9) xx 8 (4)/(5) xx 9 (2)/(3)`= ?

Options

A. 491
B. 590
C. 547
D. 460

Answer

To solve the problem step by step, we need to evaluate the expression given:

\[ 5\frac{7}{9} \times 8\frac{4}{5} \times 9\frac{2}{3} \]

### Step 1: Convert mixed numbers to improper fractions
First, we convert each mixed number to an improper fraction.

1. **Convert \( 5\frac{7}{9} \)**:
\[ 5\frac{7}{9} = \frac{5 \times 9 + 7}{9} = \frac{45 + 7}{9} = \frac{52}{9} \]

2. **Convert \( 8\frac{4}{5} \)**:
\[ 8\frac{4}{5} = \frac{8 \times 5 + 4}{5} = \frac{40 + 4}{5} = \frac{44}{5} \]

3. **Convert \( 9\frac{2}{3} \)**:
\[ 9\frac{2}{3} = \frac{9 \times 3 + 2}{3} = \frac{27 + 2}{3} = \frac{29}{3} \]

Now, we can rewrite the expression:
\[ \frac{52}{9} \times \frac{44}{5} \times \frac{29}{3} \]

### Step 2: Multiply the fractions
Next, we multiply the fractions together:
\[ \frac{52 \times 44 \times 29}{9 \times 5 \times 3} \]

### Step 3: Calculate the denominator
Calculate the denominator:
\[ 9 \times 5 \times 3 = 135 \]

### Step 4: Calculate the numerator
Now calculate the numerator \( 52 \times 44 \times 29 \):
1. First, calculate \( 52 \times 44 \):
\[ 52 \times 44 = 2288 \]

2. Now multiply by \( 29 \):
\[ 2288 \times 29 = 66352 \]

### Step 5: Combine the results
Now we have:
\[ \frac{66352}{135} \]

### Step 6: Approximate the division
Now, we need to approximate \( \frac{66352}{135} \):
1. Perform the division:
\[ 66352 \div 135 \approx 491.49 \]

### Conclusion
The approximate value that should come in place of the question mark (?) is:
\[ \approx 491 \]