Final answer:
Clancy can share approximately 9 and 5/9 servings of yogurt with his friends.
Step-by-step explanation:
To determine the number of servings of yogurt Clancy can share with his friends, we need to divide the total amount of yogurt by the amount each guest will receive. Clancy has 4 and 2/3 cups of yogurt, and each guest will receive 3/4 of a cup of yogurt. We can divide 4 and 2/3 by 3/4 to find the number of servings.
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. In this case, we multiply 4 and 2/3 by 4/3 (the reciprocal of 3/4).
4 and 2/3 * 4/3 = 22/3 * 4/3 = 88/9
So, Clancy can share approximately 9 and 5/9 servings of yogurt with his friends. Therefore, the correct option is Option 4: 8 servings.