Nat's goal was to complete 4/5 of his math problems before dinner. when dinner was served, he completed 5/7 of the problems. how much more of his assignment does he have left to do?

So here we just want to convert the fractions to have a common denominator.
The least common factor between the two is 35.
(5, 10, 15, 20, 25, 30, 35)
(7, 14, 21, 28, 35)

So now we just multiply each of the fractions to get them to have a denominator of 35.
4/5 * 7/7
28/35

5/7 * 5/5
25/35

And now we can just subtract them.
28/35 - 25/35 = 3/35

So he has 3/35 more of his assignment to go.