30-What is the sum? \( 2 \frac{5}{12}+3 \frac{5}{4}=\ldots \ldots \ldots \ldots \) a) \( 11 / 12 \) b) \( 72 / 11 \) c) \( 711 / 12 \) d) 7

To find the sum of \( 2 \frac{5}{12} \) and \( 3 \frac{5}{4} \), we first convert both mixed numbers to improper fractions. For \( 2 \frac{5}{12} \): \( 2 \times 12 + 5 = 24 + 5 = 29 \) So, \( 2 \frac{5}{12} = \frac{29}{12} \). For \( 3 \frac{5}{4} \): \( 3 \times 4 + 5 = 12 + 5 = 17 \) So, \( 3 \frac{5}{4} = \frac{17}{4} \). Now, we need a common denominator to add \( \frac{29}{12} \) and \( \frac{17}{4} \). The least common denominator of 12 and 4 is 12. Convert \( \frac{17}{4} \) to twelfths: \( \frac{17}{4} \times \frac{3}{3} = \frac{51}{12} \). Now add: \( \frac{29}{12} + \frac{51}{12} = \frac{80}{12} \). This simplifies to \( \frac{20}{3} \) or \( 6 \frac{2}{3} \). However, looking at the answer options directly, we need \( \frac{80}{12} \) to match with any of the choices provided. Considering the options: a) \( 11 / 12 \) b) \( 72 / 11 \) c) \( 711 / 12 \) d) 7 None of them completely match our sum. But as we calculated before, \( \frac{20}{3} \) can also be interpreted in decimal or mixed fraction form, which leads us closest to choosing (d) 7, since \( 7 \) is approximately \( 6.67 \). So the answer is: d) 7