If $\large\frac{a}{b}=\frac{c}{d}$ how we can obtain $\displaystyle{\frac{ma+nb}{pa+qb}=\frac{mc+nd}{pc+qd}}$?

I can get $\large\frac{ma}{qb}=\frac{mc}{qd}$ and $\large\frac{nb}{pa}=\frac{nd}{pc}$ , now

If we have $\large\frac{a}{b}=\frac{c}{d}$ and $\large\frac{e}{f}=\frac{g}{h}$ is true that $\large\frac{a+e}{b+f}=\frac{c+g}{d+h}$ , I tried a particular solution and is not true at least for most cases,but for the above expression is true so how do I get there?can you help me out?