Question

How are the products of -3(1) and - 3(-1) the same?

Answer 1

The products of -3(1) and -3(-1) are the same because both expressions result in the multiplication of -3 and a number, where one of the numbers is positive and the other is negative. The product of these two numbers is always negative.

Explanation:

-3(1) means multiplying -3 by 1, which gives -3 as the product.

-3(-1) means multiplying -3 by -1, which gives 3 as the product.

Even though the two expressions are different, we can see that both involve multiplying -3 with a number, where one of the numbers is positive and the other is negative.

When we multiply a negative number and a positive number, the product is always negative. Similarly, when we multiply a negative number and a negative number, the product is always positive.

So, in both -3(1) and -3(-1), we are multiplying a negative number (-3) with a positive number (1 in the first expression and -1 in the second expression). Therefore, the products of both expressions are negative (-3 in the first expression and 3 with a negative sign in the second expression).

Hence, we can conclude that the products of -3(1) and -3(-1) are the same and equal to -3.

Answer 2

The products of -3(1) and -3(-1) are the same because of the property of multiplication called the "multiplicative property of opposites," which states that the product of a number and its opposite is always negative. In this case, 1 and -1 are opposites, so their product is -1. Therefore, we have:

-3(1) = -3
-3(-1) = 3

Even though the numbers being multiplied are different, their opposites are the same, so the products are equal but with opposite signs. In this case, -3 and 3 are opposites, so their product is -9. Therefore, we have:

-3(1) = -9
-3(-1) = -9

So, the products of -3(1) and -3(-1) are the same and equal to -9 due to the multiplicative property of opposites.