What fraction of air gets expelled upon heating an empty flask?
Your first equation should be:
$${V_1\over V_2} = {T_1\over T_2}$$

We want to know what $V_2$ is in terms of $V_1$. Here, I call $V_2$ final volume. Arranging the equation and using the values for temperature in kelvin:
$${\rm final\;volume} = {V_1 \times 750\over 300}= {5\over 2}V_1$$

To get the amount that was expelled, we subtract the initial volume ($V_1$) from the final volume:
$${\rm amount\;expelled} = {5\over 2}V_1 - V_1 = {3\over 2}V_1$$

The fraction expelled is then:
$${{\rm amount\;expelled}\over{\rm final\;volume}} = {3\over 5} $$