Multiplication the same as addition

Number Theory Level 2

Multiplication never gives the same result as addition. Or does it?

If \(a\), \(b\), and \(c\) are non-negative integers, \(b\) and \(c\) are relatively prime, and \(a+\frac{b}{c}=a\times\frac{b}{c}\), then what is \(b-c\)?