1. **State the problem:** Simplify and identify the property used in the expression $$4 \frac{1}{3} \left( \frac{2}{5} - \frac{1}{3} \right)$$. 2. **Recall the distributive property:** The distributive property states that for any numbers $a$, $b$, and $c$, $$a(b - c) = ab - ac$$ This means you multiply $a$ by each term inside the parentheses separately. 3. **Convert mixed number to improper fraction:** $$4 \frac{1}{3} = \frac{13}{3}$$ 4. **Apply the distributive property:** $$\frac{13}{3} \left( \frac{2}{5} - \frac{1}{3} \right) = \frac{13}{3} \cdot \frac{2}{5} - \frac{13}{3} \cdot \frac{1}{3}$$ 5. **Multiply the fractions:** $$\frac{13}{3} \cdot \frac{2}{5} = \frac{26}{15}$$ $$\frac{13}{3} \cdot \frac{1}{3} = \frac{13}{9}$$ 6. **Subtract the results:** Find a common denominator for $\frac{26}{15}$ and $\frac{13}{9}$, which is 45. $$\frac{26}{15} = \frac{26 \times 3}{15 \times 3} = \frac{78}{45}$$ $$\frac{13}{9} = \frac{13 \times 5}{9 \times 5} = \frac{65}{45}$$ 7. **Perform the subtraction:** $$\frac{78}{45} - \frac{65}{45} = \frac{78 - 65}{45} = \frac{13}{45}$$ 8. **Final answer:** $$4 \frac{1}{3} \left( \frac{2}{5} - \frac{1}{3} \right) = \frac{13}{45}$$ 9. **Property used:** This is the **Distributive Property of Multiplication Over Subtraction**.