Hello, Godfather!

Here's one approach . . .What is the largest possible value for the sum of two fractions such that

each of {2, 3, 5, 7} occurs as one of the numerators or denominators?

The sum of two fractions is: .

For the largest value, we want thesmallest denominator.

. . This occurs for: . .(or vice versa).

We have: .

Then we have two choices: .

If

If

Therefore: . .is the largest sum.