156082

In this problem, you had to get the fractions as close to one whole as possible. You could use as many of the fractions as you wanted, but not the same one twice. The closest I got to a whole was 1/30 over- my answer was 31/30.
First, I read the question carefully. The six fractions we could use were 1/6, 1/25, 3/5, 3/20, 4/15 and 5/8. Logically, small numbers like 1/25 and 3/20 were not enough to make a whole number, so I started by putting together two large numbers, 1/6 and 3/5.
Adding fractions is fairly simple. you find a common denominator and scale the numerator to match. The denominator I used was 30, and after I scaled up the numerator I had 5/30 + 18/30. then you simply add the numerator, so my answer was 23/30, which was not quite enough.
I then added one of the smaller fractions as well, 4/15. 4/15 scaled up to 8/30, which, when added with 23/30 = 31/30. I tried a few other combinations as well, but 31/30 was the closest I could get.