Which correctly applies the distributive property to show an equivalent expression to (8.6)(-2.5)2
(8)(2) – (0.6)(0.5)
(8)(- 2) – (0.6)(- 0.5)
(8.6)(2) – (8.6)(0.5)
(8.6)(- 2) + (8.6)(- 0.5)
The correct answer and explanation is:
The correct application of the distributive property to show an equivalent expression for (8.6)(−2.5)(8.6)(-2.5) is:
(8.6)(-2) + (8.6)(-0.5)
Explanation:
The distributive property allows us to break a multiplication expression into smaller, easier-to-handle parts. In this case, (8.6)(−2.5)(8.6)(-2.5) is being multiplied, and we want to distribute the multiplication over the terms in −2.5-2.5.
To do this, we rewrite −2.5-2.5 as a sum of two terms: −2.5=−2+(−0.5)-2.5 = -2 + (-0.5)
Now, using the distributive property: (8.6)(−2.5)=(8.6)(−2)+(8.6)(−0.5)(8.6)(-2.5) = (8.6)(-2) + (8.6)(-0.5)
This works because when you distribute, you multiply each part of the sum separately. So, instead of multiplying 8.68.6 directly by −2.5-2.5, you multiply 8.68.6 by each part of the sum −2-2 and −0.5-0.5, and then add the results together. This gives you the same result as multiplying 8.68.6 by −2.5-2.5.
Why the other options are incorrect:
- (8)(2) – (0.6)(0.5): This does not apply the distributive property properly. It incorrectly assumes the separation of the terms within the factors.
- (8)(-2) – (0.6)(-0.5): This expression uses an incorrect approach by separating the numbers inappropriately. The distributive property should be applied to the entire number 8.68.6, not just the 88 part.
- (8.6)(2) – (8.6)(0.5): This option is incorrect because it doesn’t match the sign of −2.5-2.5, which was part of the original expression. Additionally, the distributive property should keep the correct signs.
By applying the distributive property correctly, you break down the expression into manageable parts, ensuring that all terms are accounted for and the calculation is accurate.