The word "product" tells us we need to multiply. We can call the other number that is unknown x.
15 * x = 1 1/5
15x = 1 1/5
1 1/5 = 6/5 as an improper fraction
15x = 6/5
Let's multiply both sides of the equation by 5
75x = 6
x = 6/75 = 2/25
The sum of the two number is 15 + 2/25 = 15 2/25