Question: Solve the following proportion for $v$. $$\frac{11}{13} = \frac{v}{7}$$ Round your answer to the nearest tenth.
1. **State the problem:** We need to solve the proportion $$\frac{11}{13} = \frac{v}{7}$$ for the variable $v$ and then round the answer to the nearest tenth.
2. **Recall the rule for proportions:** If $$\frac{a}{b} = \frac{c}{d}$$, then the cross products are equal: $$a \times d = b \times c$$.
3. **Apply the cross multiplication:**
$$11 \times 7 = 13 \times v$$
4. **Calculate the left side:**
$$77 = 13v$$
5. **Solve for $v$ by dividing both sides by 13:**
$$v = \frac{77}{13}$$
6. **Simplify the fraction:**
$$v = \frac{\cancel{77}}{\cancel{13}}$$ (no common factors to cancel, so it remains $$\frac{77}{13}$$)
7. **Convert to decimal:**
$$v \approx 5.923076923$$
8. **Round to the nearest tenth:**
$$v \approx 5.9$$
**Final answer:** $$v = 5.9$$