1. **State the problem:** We need to find the missing number in the equation: $$15 \frac{3}{8} - 13 \frac{7}{8} = 1 \frac{7}{8}$$ 2. **Convert mixed numbers to improper fractions:** $$15 \frac{3}{8} = \frac{15 \times 8 + 3}{8} = \frac{120 + 3}{8} = \frac{123}{8}$$ $$13 \frac{7}{8} = \frac{13 \times 8 + 7}{8} = \frac{104 + 7}{8} = \frac{111}{8}$$ $$1 \frac{7}{8} = \frac{1 \times 8 + 7}{8} = \frac{8 + 7}{8} = \frac{15}{8}$$ 3. **Rewrite the equation with improper fractions:** $$\frac{123}{8} - 13 \frac{7}{8} = \frac{15}{8}$$ 4. **Isolate the missing number (let it be $x$):** $$\frac{123}{8} - x = \frac{15}{8}$$ 5. **Solve for $x$ by subtracting $\frac{15}{8}$ from $\frac{123}{8}$:** $$x = \frac{123}{8} - \frac{15}{8}$$ 6. **Subtract the fractions:** $$x = \frac{123 - 15}{8} = \frac{108}{8}$$ 7. **Simplify the fraction by dividing numerator and denominator by 4:** $$x = \frac{\cancel{108}^{{\div 4}}}{\cancel{8}^{{\div 4}}} = \frac{27}{2}$$ 8. **Convert back to a mixed number:** $$\frac{27}{2} = 13 \frac{1}{2}$$ **Final answer:** The missing number is $13 \frac{1}{2}$.