Question: Find the unknown number in the proportion. Reduce your answer to lowest terms.
$$\frac{7}{n} = \frac{4}{\frac{9}{4}}$$
1. **State the problem:** We need to find the unknown number $n$ in the proportion $$\frac{7}{n} = \frac{4}{\frac{9}{4}}$$ and reduce the answer to lowest terms.
2. **Understand the proportion:** A proportion states that two ratios are equal. Here, $$\frac{7}{n}$$ is equal to $$\frac{4}{\frac{9}{4}}$$.
3. **Simplify the right side:** The denominator on the right side is a fraction $$\frac{9}{4}$$, so dividing by $$\frac{9}{4}$$ is the same as multiplying by its reciprocal:
$$\frac{4}{\frac{9}{4}} = 4 \times \frac{4}{9} = \frac{16}{9}$$
4. **Rewrite the proportion:** Now the equation is
$$\frac{7}{n} = \frac{16}{9}$$
5. **Cross multiply:** Multiply both sides to eliminate the fractions:
$$7 \times 9 = 16 \times n$$
which gives
$$63 = 16n$$
6. **Solve for $n$:** Divide both sides by 16:
$$n = \frac{63}{16}$$
7. **Check if fraction can be reduced:** 63 and 16 have no common factors other than 1, so the fraction is already in lowest terms.
**Final answer:**
$$n = \frac{63}{16}$$