Mediant is Between/Corollary 2/Proof 3

Corollary to Mediant is Between

Let $a, b, c, d \in \R$ be real numbers such that $b > 0, d > 0$.

Let $\dfrac a b = \dfrac c d$.

Then:

$\dfrac a b = \dfrac {a + c} {b + d} = \dfrac c d$

Proof

Let:

$t := \dfrac a b = \dfrac c d$

Then:

$a = t c$

and:

$c = t d$

Hence:

$\dfrac {a + b}{c + d} = \dfrac {t \paren {c + d} }{c + d} = t$

$\blacksquare$