a. $\frac{a}{b}$ = $\frac{c}{d}$
<-> $\frac{c}{a}$ = $\frac{d}{b}$
<-> $\frac{c}{a-c}$ = $\frac{d}{b-d}$
b. $\frac{a}{b}$ = $\frac{c}{d}$
<-> $\frac{a}{c}$ = $\frac{b}{d}$= $\frac{a+b}{c+d}$
c. $\frac{a}{b}$ = $\frac{c}{d}$=$\frac{2a}{2b}$ = $\frac{3c}{3d}$=$\frac{-3c}{-3d}$=$\frac{2a+3c}{2b+3d}$= $\frac{2a-3c}{2b-3d}$