\( \mathrm{d} 15 \frac{1}{4}+11 \frac{1}{7}+8 \frac{1}{6} \). Simplify the answer and write as a reduced mixed number.

To simplify \( \mathrm{d} 15 \frac{1}{4}+11 \frac{1}{7}+8 \frac{1}{6} \), we first convert each mixed number into an improper fraction. 1. \( 15 \frac{1}{4} = 15 \cdot 4 + 1 = 60 + 1 = \frac{61}{4} \) 2. \( 11 \frac{1}{7} = 11 \cdot 7 + 1 = 77 + 1 = \frac{78}{7} \) 3. \( 8 \frac{1}{6} = 8 \cdot 6 + 1 = 48 + 1 = \frac{49}{6} \) Next, we need a common denominator to add these fractions. The least common multiple (LCM) of 4, 7, and 6 is 84. Now, we convert each fraction: 1. \(\frac{61}{4} = \frac{61 \times 21}{4 \times 21} = \frac{1281}{84}\) 2. \(\frac{78}{7} = \frac{78 \times 12}{7 \times 12} = \frac{936}{84}\) 3. \(\frac{49}{6} = \frac{49 \times 14}{6 \times 14} = \frac{686}{84}\) Now we can sum these fractions: \[ \frac{1281}{84} + \frac{936}{84} + \frac{686}{84} = \frac{1281 + 936 + 686}{84} = \frac{2903}{84} \] Now, we convert the improper fraction \( \frac{2903}{84} \) into a mixed number. We divide \( 2903 \) by \( 84 \): \[ 2903 \div 84 \approx 34.5 \] This means we have \( 34 \) full parts and a remainder. Calculating the remainder: \[ 34 \times 84 = 2856 \] \[ 2903 - 2856 = 47 \] So we can express \( \frac{2903}{84} \) as a mixed number: \[ 34 \frac{47}{84} \] Now, check if \( \frac{47}{84} \) can be reduced. Since \( 47 \) is a prime number and does not divide \( 84 \), the fraction is already in its simplest form. Thus, the final simplified answer is: \[ 34 \frac{47}{84} \]