`(1)/(5)xx(5)/(7)div (6)/(7)=?`

Options

A. `1/5`
B. `3/5`
C. `1/6`
D. `2/7`

Explanation

To solve the expression \( \frac{1}{5} \times \frac{5}{7} \div \frac{6}{7} \), we will follow these steps:

### Step 1: Rewrite the Division as Multiplication
The division of fractions can be rewritten as multiplication by the reciprocal. Therefore, we can rewrite the expression as:
\[ \frac{1}{5} \times \frac{5}{7} \times \frac{7}{6} \]

### Step 2: Multiply the Fractions
Now, we will multiply the fractions together. When multiplying fractions, we multiply the numerators together and the denominators together:
\[ \frac{1 \times 5 \times 7}{5 \times 7 \times 6} \]

### Step 3: Simplify the Expression
Now we can simplify the expression. Notice that the \(5\) in the numerator and denominator cancels out, as well as the \(7\):
\[ \frac{1 \times \cancel{5} \times \cancel{7}}{\cancel{5} \times \cancel{7} \times 6} = \frac{1}{6} \]

### Final Answer
Thus, the value of the expression is:
\[ \frac{1}{6} \]