Solve the Fraction Equation: Finding the Factor in 5/7 × ? = 1/3

To solve this problem, we'll proceed with the following steps:

• Step 1: Set up the equation: $\frac{5}{7} \times x = \frac{1}{3}$.
• Step 2: Isolate $x$ by dividing both sides by $\frac{5}{7}$, which is equivalent to multiplying both sides by the reciprocal, $\frac{7}{5}$.
• Step 3: Simplify the resulting expression to find $x$.

Now, applying these steps:
Step 1: We have the equation $\frac{5}{7} \times x = \frac{1}{3}$.
Step 2: Multiply both sides by $\frac{7}{5}$ to isolate $x$:
$x = \frac{1}{3} \times \frac{7}{5}$.
Step 3: Simplify the calculation:
$x = \frac{1 \times 7}{3 \times 5} = \frac{7}{15}$.

Therefore, the solution to the problem is $x = \frac{7}{15}$.