`(3)/(7)xx(9)/(14) div (5)/(7)=?`

Options

A. `(27)/(70)`
B. `(13)/(35)`
C. `(17)/(70)`
D. `(12)/(35)`

Explanation

To solve the expression \(\frac{3}{7} \times \frac{9}{14} \div \frac{5}{7}\), we will follow these steps:

### Step 1: Rewrite the division as multiplication
The division of fractions can be rewritten as multiplication by the reciprocal. Thus, we can rewrite the expression as:
\[ \frac{3}{7} \times \frac{9}{14} \times \frac{7}{5} \]

### Step 2: Multiply the fractions
Now we will multiply the fractions together. We can multiply the numerators and the denominators:
\[ \frac{3 \times 9 \times 7}{7 \times 14 \times 5} \]

### Step 3: Simplify the expression
Before multiplying, we can simplify the expression by canceling out the common factors. The \(7\) in the numerator and denominator cancels out:
\[ \frac{3 \times 9}{14 \times 5} \]

### Step 4: Calculate the numerator and denominator
Now we calculate the numerator and denominator:
- The numerator: \(3 \times 9 = 27\)
- The denominator: \(14 \times 5 = 70\)

So we have:
\[ \frac{27}{70} \]

### Final Answer
Thus, the value of the expression is:
\[ \frac{27}{70} \]

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