Question

The following question has two parts. First, answer part A. Then, answer part B. The following information applies to both parts.

Dario purchased a party size sub, and he decides to share it with 3 of his friends. So, he cuts the sub into 4 equal pieces. However, another one of his friends also showed up, and there are now 5 people in total.

Part A
Now that the sub will be shared equally among 5 people, will each person get more or less sub? Briefly state why you think so.

(1 point)

Part B
Dario decides to take each one of the 4 pieces and share it equally among the 5 of them. First, he divides one piece into 5 equal parts and shares it, then the next one, and so on.

What fraction of the party size sub did each person get after all the parts were shared out? Briefly explain your reasoning.

(2 points)

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Answer 1

Part A
Each person gets less. Originally each would get 1/4 of the sub; with 5 people each would get 1/5, and 1/5 < 1/4.

Part B
Each of the 4 pieces is split into 5, so from one piece each person gets (1/4)·(1/5) = 1/20. From all 4 pieces each person gets 4·(1/20) = 4/20 = 1/5 of the whole sub.