Question: Find the unknown number in the proportion.
$$\frac{13}{14} = \frac{x}{111}$$
Round your answer to the nearest hundredth.
1. **State the problem:** We need to find the unknown number $x$ in the proportion $$\frac{13}{14} = \frac{x}{111}$$.
2. **Formula used:** In a proportion $$\frac{a}{b} = \frac{c}{d}$$, the cross products are equal, so $$a \times d = b \times c$$.
3. **Apply the formula:** Here, $$13 \times 111 = 14 \times x$$.
4. **Calculate the left side:** $$13 \times 111 = 1443$$.
5. **Set up the equation:** $$1443 = 14 \times x$$.
6. **Solve for $x$ by dividing both sides by 14:**
$$x = \frac{1443}{14}$$
7. **Show cancellation:**
$$x = \frac{\cancel{1443}}{\cancel{14}}$$ (no common factors to cancel, so just division)
8. **Calculate the division:**
$$x = 103.0714...$$
9. **Round to the nearest hundredth:**
$$x \approx 103.07$$.
**Final answer:** $$x = 103.07$$.