Question

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

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.