Find the reciprocal of \( 4 \frac{1}{6} \). The reciprocal of \( 4 \frac{1}{6} \) is \( \square \). (Type an integer or a fraction.)

To find the reciprocal of \( 4 \frac{1}{6} \), first convert the mixed number to an improper fraction. Step 1: Multiply the whole number (4) by the denominator (6): \( 4 \times 6 = 24 \). Step 2: Add the numerator (1) to the result: \( 24 + 1 = 25 \). Step 3: Write this as an improper fraction: \( 4 \frac{1}{6} = \frac{25}{6} \). Now, the reciprocal is obtained by flipping the fraction: \(\frac{6}{25}\). So, the reciprocal of \( 4 \frac{1}{6} \) is \( \frac{6}{25} \).