What is the value of \( m \) in this proportion? \( \frac{\frac{1}{7}}{\frac{7}{4}}=\frac{\frac{1}{6}}{m} \) Enter your answer as a fraction in simplest form in the box. \( m=\square \)

To solve for \( m \) in the proportion \( \frac{\frac{1}{7}}{\frac{7}{4}}=\frac{\frac{1}{6}}{m} \), we can use cross-multiplication. This gives us: \[ \frac{1}{7} \cdot m = \frac{1}{6} \cdot \frac{7}{4} \] Calculating the right side: \[ \frac{1}{6} \cdot \frac{7}{4} = \frac{7}{24} \] Now, substituting this back gives us: \[ \frac{m}{7} = \frac{7}{24} \] Next, we multiply both sides by 7 to isolate \( m \): \[ m = \frac{7}{24} \cdot 7 = \frac{49}{24} \] Thus, the value of \( m \) in simplest form is: \[ m = \frac{49}{24} \]