1. **State the problem:** Simplify the expression $\frac{9}{4} - 1$. 2. **Recall the rule:** To subtract a whole number from a fraction, convert the whole number to a fraction with the same denominator. 3. Convert $1$ to $\frac{4}{4}$ because the denominator of $\frac{9}{4}$ is $4$. 4. Rewrite the expression: $$\frac{9}{4} - \frac{4}{4}$$ 5. Subtract the numerators: $$\frac{9 - 4}{4} = \frac{5}{4}$$ 6. The simplified result is $\frac{5}{4}$ or $1 \frac{1}{4}$ in mixed number form.