Which equation shows how the properties of numbers extend to negative whole numbers by the Distributive Property?
A) −2 + 4 = 4 + (−2)
B) −2(4) = 4(−2)
C) (−2 + 4) + 3 = −2 + (4 + 3)
D) −2(4 + 3) = (−2 x 4) + (−2 x 3)
well, the distributive property says that a(b+c) = ab + ac
So, which choice follows that pattern?
The Distributive Property states that for any real numbers a, b, and c, the equation a(b + c) = ab + ac holds true. It tells us that we can distribute the factor a to each term inside the parentheses.
To find the equation that shows how the properties of numbers extend to negative whole numbers by the Distributive Property, we need to check each option and see which one demonstrates the property.
Let's analyze the given options:
A) −2 + 4 = 4 + (−2)
This equation shows the commutative property of addition, not the distributive property. The numbers are simply rearranged, but the distribution does not occur.
B) −2(4) = 4(−2)
This equation represents the commutative property of multiplication, not the distributive property. Again, the numbers are switched around, but the distribution is not present.
C) (−2 + 4) + 3 = −2 + (4 + 3)
This equation is an example of the associative property of addition. It shows that the grouping of terms can be changed without altering the sum. Therefore, this option does not demonstrate the distributive property.
D) −2(4 + 3) = (−2 x 4) + (−2 x 3)
This equation depicts the distributive property. We have a factor of −2 being distributed to the terms inside the parentheses (4 and 3), and then multiplied with each term separately.
Therefore, the correct option is D) −2(4 + 3) = (−2 x 4) + (−2 x 3), which demonstrates the properties of numbers extending to negative whole numbers through the distributive property.