What approximate value should come in place of the question mark(?) in the following question (?)
(You are not expected to calculate the exact value )
`4/5 xx 3/7 div 6/7 div 5/9=?`

Options

A. `9/(17)`
B. `(20)/(49)`
C. `(18)/(25)`
D. `1/2`

Answer

To solve the expression \( \frac{4}{5} \times \frac{3}{7} \div \frac{6}{7} \div \frac{5}{9} \) and find the approximate value for the question mark (?), we can follow these steps:

### Step 1: Rewrite the expression
The expression can be rewritten as:
\[ \frac{4}{5} \times \frac{3}{7} \div \frac{6}{7} \div \frac{5}{9} \]
This can be interpreted as:
\[ \frac{4}{5} \times \frac{3}{7} \times \frac{7}{6} \times \frac{9}{5} \]

### Step 2: Simplify the divisions
When dividing by a fraction, we multiply by its reciprocal. Thus, we change the divisions into multiplications:
\[ \frac{4}{5} \times \frac{3}{7} \times \frac{7}{6} \times \frac{9}{5} \]

### Step 3: Cancel common factors
Notice that \( \frac{3}{7} \) and \( \frac{7}{6} \) can be simplified:
- The \( 7 \) in the numerator of \( \frac{3}{7} \) cancels with the \( 7 \) in the denominator of \( \frac{7}{6} \).

So now we have:
\[ \frac{4}{5} \times \frac{3}{6} \times \frac{9}{5} \]

### Step 4: Simplify further
Now simplify \( \frac{3}{6} \) to \( \frac{1}{2} \):
\[ \frac{4}{5} \times \frac{1}{2} \times \frac{9}{5} \]

### Step 5: Multiply the fractions
Now we multiply the fractions together:
\[ \frac{4 \times 1 \times 9}{5 \times 2 \times 5} = \frac{36}{50} \]

### Step 6: Simplify the final fraction
Now simplify \( \frac{36}{50} \):
\[ \frac{36 \div 2}{50 \div 2} = \frac{18}{25} \]

### Conclusion
Thus, the approximate value that should come in place of the question mark (?) is:
\[ \frac{18}{25} \]