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 1-foot long piece of gum did each person get after all the parts were shared out? Briefly explain your reasoning.

1/5.

If 4 pieces of gum are each divided into 5 parts, that will mean there will be 20 smaller parts (5*4=20).

Each person will get one part of each piece of gum. If there are 4 pieces of gum originally, this means each person gets 4 small pieces of gum

If each person gets 4 small pieces of gum and there are 20 small pieces altogether, that makes the fraction 4/20

Since 4 and 20 are both divisible by 4, that makes the simplified answer 1/5.