students in a cooking class made 4 1/2 quarts of soup.They served 4/5 of the soup to friends.Each serving is 3/5 quart.Hector incorrectly says that there were 3 3/5 serving of soup.What is the correct number of servings ? what did Hector do wrong ?

so the students mad 4 and 1/2 quarts of soup.

they served 4/5 of that 4 and 1/2 to some friends....well, what's 4/5 of 4 and 1/2?  well is just their product.

[tex]\bf 4\frac{1}{2}\implies \cfrac{4\cdot 2+1}{2}\implies \cfrac{9}{2}\qquad\qquad \qquad \qquad \cfrac{9}{2}\cdot \cfrac{4}{5}\implies \cfrac{18}{5}[/tex]

so, each friend got to drink 3/5 quart, how many servings, and therefore friends, can one get out of 18/5 quarts of soup?

well, how many times does 3/5 go into 18/5?  let's check.

[tex]\bf \cfrac{\quad \frac{18}{5}\quad }{\frac{3}{5}}\implies \cfrac{18}{\underline{5}}\cdot \cfrac{\underline{5}}{3}\implies \cfrac{18}{3}\implies \stackrel{servings}{6}[/tex]

so, there were 6 servings, meaning there were 6 friends about.

now, whatever happened to Hector?   well, 18/5 in mixed is 3 and 3/5, so he's correct, there were 3 and 3/5 "quarts in total" served to the friends, but each serving wasn't that much, was just a fraction of that.