Four friends decided to buy and share a pizza to eat during a football game. The first friend ate 1/5 of the pizza, the second ate 3/5 of the rest and the third, 1/3 of what was left after the second friend ate his share. The fourth friend waited for everyone to eat before taking the rest of the pizza. Considering that there was no waste, let a/b be the irreducible fraction that represents the amount of pizza that the fourth friend ate. Q

ANSWER: First friend ate $$ \frac{1}{5} $$of the pizza . So the rest is $$ 1-\frac{1}{5}=\frac{4}{5} $$of the the pizza. Hence Second friend ate $$ \frac{4}{5}\times\frac{3}{5}=\frac{12}{25} $$ of the pizza. So the rest after second friend ate is $$ \frac{4}{5}-\frac{12}{25}=\frac{\left(20-12\right)}{25}=\frac{8}{25} $$of the pizza. Third friend ate $$ \frac{8}{25}\times\frac{1}{3}=\frac{8}{75} $$of the pizza. Rest is $$ \frac{8}{5}-\frac{8}{75}=\frac{24-8}{75}=\frac{16}{75} $$of the pizza. Fourth friend ate $$ \frac{16}{75} $$of the pizza