Final answer:
The reciprocal of the mixed number 1 1/6 is 6/7.
Step-by-step explanation:
To find the reciprocal of a mixed number, we first convert it to an improper fraction. For the mixed number 1 1/6, we multiply the whole number (1) by the denominator (6) and add the numerator (1) to get the numerator of the improper fraction. The denominator remains the same. So, the improper fraction is (6 + 1)/6 = 7/6. To find the reciprocal, we invert the fraction by swapping the numerator and denominator. Therefore, the reciprocal of 1 1/6 is 6/7.