Prove that $\min{\left(\frac{a_1}{b_1},\frac{a_2}{b_2}\right)}\leq\frac{a_1+a_2}{b_1+b_2}\leq\max{\left(\frac{a_1}{b_1},\frac{a_2}{b_2}\right)}$
Given 4 integers, $a, b, c, d > 0$, does $\frac{a}{b} < \frac{c}{d}$ imply $\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$?