1. **State the problem:** Solve the multiplication $4 \times 38$ using the distributive property. 2. **Formula and rule:** The distributive property states that for any numbers $a$, $b$, and $c$, $$a(b + c) = ab + ac$$ This means you can break down a multiplication into smaller parts that are easier to calculate. 3. **Apply the distributive property:** Break 38 into 30 and 8: $$4 \times 38 = 4 \times (30 + 8)$$ Using the distributive property: $$= 4 \times 30 + 4 \times 8$$ 4. **Calculate each part:** $$4 \times 30 = 120$$ $$4 \times 8 = 32$$ 5. **Add the results:** $$120 + 32 = 152$$ 6. **Final answer:** $$4 \times 38 = 152$$ This method helps simplify multiplication by breaking it into easier parts.