Half of a large pizza is cut into 4 equal-sized pieces, and the other half is cut into 6 equal-sized pieces. If a person were to eat 1 of the large pieces and 2 of the smaller pieces, what fraction of the pizza would remain uneaten?

~$\frac{5}{12}$~

~$\frac{13}{24}$~

~$\frac{7}{12}$~

~$\frac{2}{3}$~

~$\frac{17}{24}$~