1. **State the problem:** Simplify the expression $1 \frac{7}{8} \times 2v$. 2. **Convert the mixed number to an improper fraction:** $$1 \frac{7}{8} = \frac{8 \times 1 + 7}{8} = \frac{15}{8}$$ 3. **Rewrite the expression using the improper fraction:** $$\frac{15}{8} \times 2v$$ 4. **Multiply the fractions and variables:** $$\frac{15}{8} \times 2v = \frac{15 \times 2v}{8} = \frac{30v}{8}$$ 5. **Simplify the fraction by dividing numerator and denominator by their greatest common divisor (2):** $$\frac{\cancel{30}^{{15}}v}{\cancel{8}^{{4}}} = \frac{15v}{4}$$ 6. **Final simplified expression:** $$\frac{15v}{4}$$ This means the expression $1 \frac{7}{8} \times 2v$ simplifies to $\frac{15v}{4}$, which is the simplest form.