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 larger pieces and 2 of the smaller pieces, what fraction of the pizza would remain uneaten?
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A$$\frac{5}{12}$$
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B$$\frac{13}{24}$$
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C$$\frac{7}{12}$$
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D$$\frac{2}{3}$$
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E$$\frac{17}{24}$$