1. **State the problem:** We need to find the sum of the fractions $\frac{1}{8} + \frac{1}{7} + \frac{2}{7} + \frac{7}{8}$. 2. **Formula and rules:** To add fractions, we need a common denominator. For fractions with different denominators, find the least common denominator (LCD), convert each fraction, then add the numerators. 3. **Find the LCD:** The denominators are 8 and 7. The LCD of 8 and 7 is $8 \times 7 = 56$ because 8 and 7 are coprime. 4. **Convert each fraction to have denominator 56:** $\frac{1}{8} = \frac{1 \times 7}{8 \times 7} = \frac{7}{56}$ $\frac{1}{7} = \frac{1 \times 8}{7 \times 8} = \frac{8}{56}$ $\frac{2}{7} = \frac{2 \times 8}{7 \times 8} = \frac{16}{56}$ $\frac{7}{8} = \frac{7 \times 7}{8 \times 7} = \frac{49}{56}$ 5. **Add the converted fractions:** $$\frac{7}{56} + \frac{8}{56} + \frac{16}{56} + \frac{49}{56} = \frac{7 + 8 + 16 + 49}{56} = \frac{80}{56}$$ 6. **Simplify the fraction:** Find the greatest common divisor (GCD) of 80 and 56, which is 8. $$\frac{\cancel{8} \times 10}{\cancel{8} \times 7} = \frac{10}{7}$$ 7. **Final answer:** $$\frac{1}{8} + \frac{1}{7} + \frac{2}{7} + \frac{7}{8} = \frac{10}{7}$$ This is an improper fraction and can also be written as $1 \frac{3}{7}$.