1. **State the problem:** We need to estimate and then find the exact difference of the mixed numbers $2 \frac{1}{4}$ and $1 \frac{3}{5}$. 2. **Convert mixed numbers to improper fractions:** $$2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}$$ $$1 \frac{3}{5} = \frac{1 \times 5 + 3}{5} = \frac{8}{5}$$ 3. **Estimate the difference:** Estimate $2 \frac{1}{4} \approx 2.25$ and $1 \frac{3}{5} \approx 1.6$. Difference estimate: $2.25 - 1.6 = 0.65$ 4. **Find the exact difference:** $$\frac{9}{4} - \frac{8}{5}$$ Find common denominator $20$: $$\frac{9}{4} = \frac{9 \times 5}{4 \times 5} = \frac{45}{20}$$ $$\frac{8}{5} = \frac{8 \times 4}{5 \times 4} = \frac{32}{20}$$ 5. **Subtract the fractions:** $$\frac{45}{20} - \frac{32}{20} = \frac{45 - 32}{20} = \frac{13}{20}$$ 6. **Convert back to decimal:** $$\frac{13}{20} = 0.65$$ 7. **Conclusion:** The estimate and exact difference both equal $0.65$.