Final answer:
To calculate 4 2/5 times 10 using the Distributive Property, first convert 4 2/5 to an improper fraction (22/5), then distribute the multiplication across the fraction and simplify to reach the final answer of 44.
Step-by-step explanation:
The question asks to calculate 4 2/5 times 10 using the Distributive Property. The Distributive Property states that for any numbers a, b, and c, the equation a(b + c) = ab + ac holds true. To apply this to the given problem, we first convert 4 2/5 to an improper fraction, which is 22/5. Then we distribute the multiplication over the fraction:
22/5 × 10 = (20/5 + 2/5) × 10 = 20/5 × 10 + 2/5 × 10 = 40 + 4 = 44
Step-by-step explanation using the Distributive Property:
- Convert 4 2/5 to an improper fraction: 4 × 5 + 2 = 20 + 2 = 22, so 4 2/5 = 22/5.
- Multiply each term inside the parentheses by 10 using the Distributive Property: (20/5)× 10 + (2/5)× 10.
- Simplify each term: 20× 2 + 2× 2 = 40 + 4.
- Add the results together to obtain the final answer: 40 + 4 = 44.