\[3\ :1\frac{1}{2} + 5\ :1\frac{1}{4} = 3\ :\frac{3}{2} + 5\ :\frac{5}{4} =\]
\[= \frac{3 \cdot 2}{3} + \frac{5 \cdot 4}{5} = 2 + 4 = 6\]