# Simplifiable

**Number Theory**Level 3

Let us take two fractions \(\dfrac{a}{b}\) and \(\dfrac{c}{d}\), where \(a,b,c\) and \(d\) are pairwise coprime positive integers.

When is \(\dfrac{ad+cb}{bd}\) *simplifiable*? That is, when the numerator and denominator are divisible by the same number? Find the number of all such quadruplets \((a,b,c,d)\) where \(a,b,c,d<16\).