Find the sum. \[ 12 \frac{5}{16}+2 \frac{1}{4} \] Find the sum. \( 12 \frac{5}{4}+2 \frac{1}{6}=\square \)
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To find the sum \( 12 \frac{5}{16} + 2 \frac{1}{4} \), first convert the mixed numbers into improper fractions. 1. \( 12 \frac{5}{16} = \frac{12 \times 16 + 5}{16} = \frac{192 + 5}{16} = \frac{197}{16} \). 2. \( 2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \). Next, find a common denominator to add \( \frac{197}{16} \) and \( \frac{9}{4} \). The common denominator is 16. Convert \( \frac{9}{4} \) to sixteenths: \( \frac{9}{4} = \frac{9 \times 4}{4 \times 4} = \frac{36}{16} \). Now, add the two fractions: \[ \frac{197}{16} + \frac{36}{16} = \frac{197 + 36}{16} = \frac{233}{16}. \] Convert the improper fraction back to a mixed number: \[ 233 \div 16 = 14 \text{ remainder } 9. \] Thus, \( \frac{233}{16} = 14 \frac{9}{16} \). So the answer is \( 14 \frac{9}{16} \). Now for \( 12 \frac{5}{4} + 2 \frac{1}{6} \): 1. \( 12 \frac{5}{4} = \frac{12 \times 4 + 5}{4} = \frac{48 + 5}{4} = \frac{53}{4} \). 2. \( 2 \frac{1}{6} = \frac{2 \times 6 + 1}{6} = \frac{12 + 1}{6} = \frac{13}{6} \). The common denominator for \( \frac{53}{4} \) and \( \frac{13}{6} \) is 12. Convert both fractions: \[ \frac{53}{4} = \frac{53 \times 3}{4 \times 3} = \frac{159}{12}, \] \[ \frac{13}{6} = \frac{13 \times 2}{6 \times 2} = \frac{26}{12}. \] Now add the fractions: \[ \frac{159}{12} + \frac{26}{12} = \frac{159 + 26}{12} = \frac{185}{12}. \] Convert back to a mixed number: \[ 185 \div 12 = 15 \text{ remainder } 5. \] Thus, \( \frac{185}{12} = 15 \frac{5}{12} \). So the answer is \( 15 \frac{5}{12} \).