Fractions and how to solve them

Question

The sum of two negative fractions with different denominators is -7/10. What are two possible fractions and how do you find them?

Answer 1

Well, the common denominator is 10 = 2 * 5

A/5 + B/2 = -7/10

2A + 5B = -7

A and B must be integers

2(-1) + 5(-1) = -7

so the fractions are -1/5 + -1/2