Question

12. Carmen multiplied a non-zero rational number by its additive inverse. Which statement about the product must be true?

A. The product was the multiplicative inverse of the original number.

B. The product was the additive inverse of the original number.

C. The product was negative.

D. The product was positive.

Answer 1

Answer:

Option C. The product was negative.

Step-by-step explanation:

Let the non-zero rational number is = $\frac{x}{y}$

So, its additive inverse = $-\frac{x}{y}$

The result of multiplication the non-zero rational number by its additive inverse = $\frac{x}{y} *-\frac{x}{y} =-\frac{x^2}{y^2}$

We will check the options:

A. The product was the multiplicative inverse of the original number.

Wrong because the product = $\frac{x}{y} *-\frac{x}{y} =-\frac{x^2}{y^2}$

B. The product was the additive inverse of the original number.

Wrong because the product = $\frac{x}{y} *-\frac{x}{y} =-\frac{x^2}{y^2}$

C. The product was negative.

True

D. The product was positive.

Wrong because the product was negative.

So, the answer is option C.

Answer 2

Answer: c do it step by step