1. **State the problem:** Simplify the expression $\frac{9}{4} - \frac{3}{4} \times \frac{10}{3} \div \frac{5}{2}$. 2. **Recall the order of operations:** Multiplication and division are performed before subtraction, from left to right. 3. **Calculate the multiplication:** $$\frac{3}{4} \times \frac{10}{3} = \frac{3 \times 10}{4 \times 3} = \frac{30}{12} = \frac{5}{2}$$ 4. **Calculate the division:** $$\frac{5}{2} \div \frac{5}{2} = \frac{5}{2} \times \frac{2}{5} = \frac{5 \times 2}{2 \times 5} = \frac{\cancel{5} \times \cancel{2}}{\cancel{2} \times \cancel{5}} = 1$$ 5. **Substitute back into the expression:** $$\frac{9}{4} - 1$$ 6. **Convert 1 to a fraction with denominator 4:** $$1 = \frac{4}{4}$$ 7. **Perform the subtraction:** $$\frac{9}{4} - \frac{4}{4} = \frac{9 - 4}{4} = \frac{5}{4}$$ **Final answer:** $\frac{5}{4}$