The mediant of two fractions

For two positive fractions \(\dfrac{a}{b}\) and \(\dfrac{c}{d}\), where \(a\), \(b\), \(c\) and \(d\) are positive integers, the fraction \(\dfrac{a+c}{b+d}\) is called their mediant.

1. Find the mediant of \(\dfrac37\) and \(\dfrac49\), and show that it lies between \(\dfrac37\) and \(\dfrac49\).[3]
2. Given that \(\dfrac ab<\dfrac cd\), show that \(\dfrac ab<\dfrac{a+c}{b+d}\).[3]
3. Hence write down a fraction that lies strictly between \(\dfrac{5}{12}\) and \(\dfrac37\).[1]