Final answer:
To solve the division problem 4 1/3 divided by 5 1/6, find the reciprocal of the divisor 5 1/6, which is 6/5 1. Then, multiply the dividend (4 1/3) by the reciprocal of the divisor (6/5 1) to get the final answer.
Step-by-step explanation:
To solve the division problem 4 1/3 divided by 5 1/6, we need to find the reciprocal of the divisor. The reciprocal of a fraction is obtained by flipping the fraction upside-down. In this case, we need to find the reciprocal of 5 1/6, which is 6/5 1.
Now, we can multiply the dividend (4 1/3) by the reciprocal of the divisor (6/5 1). When multiplying fractions, we multiply the numerators together and the denominators together. With the given problem, the multiplication would look like this:
(4 1/3) * (6/5 1) = [((4*3)+1)/3] * [5 1/6/6] = [(12+1)/3] * [5/((6*5)+1)] = [13/3] * [5/31]
The resulting fraction, 13/3 * 5/31, cannot be simplified further. So, the answer to the division problem is 13/3 * 5/31.