To find the sum of (12 \frac{1}{4}) and (4 \frac{2}{3}), first convert both mixed numbers to improper fractions. (12 \frac{1}{4} = \frac{49}{4}) and (4 \frac{2}{3} = \frac{14}{3}). To add them, find a common denominator, which is 12:
(\frac{49}{4} = \frac{147}{12}) and (\frac{14}{3} = \frac{56}{12}).
Now, add the fractions: (\frac{147}{12} + \frac{56}{12} = \frac{203}{12}), which simplifies to (16 \frac{11}{12}).
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