1. Problem: Add the fractions $\frac{1}{8} + \frac{7}{4} + \frac{3}{7}$. 2. To add fractions, find a common denominator. The denominators are 8, 4, and 7. 3. The least common denominator (LCD) is the least common multiple of 8, 4, and 7. 4. $\mathrm{LCM}(8,4,7) = 56$. 5. Convert each fraction to have denominator 56: $$\frac{1}{8} = \frac{1 \times 7}{8 \times 7} = \frac{7}{56}$$ $$\frac{7}{4} = \frac{7 \times 14}{4 \times 14} = \frac{98}{56}$$ $$\frac{3}{7} = \frac{3 \times 8}{7 \times 8} = \frac{24}{56}$$ 6. Now add the numerators: $$\frac{7}{56} + \frac{98}{56} + \frac{24}{56} = \frac{7 + 98 + 24}{56} = \frac{129}{56}$$ 7. Simplify if possible. Since 129 and 56 share no common factors other than 1, the fraction is in simplest form. 8. Convert to mixed number: $$129 \div 56 = 2 \text{ remainder } 17$$ So, $$\frac{129}{56} = 2 \frac{17}{56}$$ **Final answer:** $\boxed{2 \frac{17}{56}}$