Question

6) Find the product of additive inverse and multiplicative inverse of -2 by3​

Answer 1

Answer:

Additive inverse of a number x is -x such that x+(-x)= 0

Multiplicative inverse of x is 1/x such that x*1/x=1

so additive inverse of -2/3 is 2/3

Multiplicative inverse of -2/3 is -3/2

So 2/3*-3/2= -1

Answer 2

Answer:

The multiplicative inverse of $\frac{-2}{3}$ is $\frac{-3}{2}$ and  the additive inverse of $\frac{-2}{3}$ is $\frac{2}{3}$

Step-by-step explanation:

Explanation:

• Additive inverse - The number that produces zero when added by $a^{-1}$ is known as the additive inverse of a number, or a, in mathematics. The opposite, a shift in the sign, and negation are other names for this number.

• Example -   The additive inverse of $\frac{-19}{6}$ is $\frac{19}{6}$

Now, given in the question that, $\frac{-2}{3}$.

So, the additive inverse of $\frac{-2}{3}$ is $\frac{2}{3}$

• Multiplicative inverse- A multiplicative inverse or reciprocal for a number x is a number that, when multiplied by x, produces the multiplicative identity, or 1. It is denoted by $\frac{1}{x}$ or $x^{-1}$.

• Example - A fraction $\frac{a}{b}$has a multiplicative inverse of $\frac{b}{a}$.

From the question we have, $\frac{-2}{3}$

So, the multiplicative inverse of $\frac{-2}{3}$ is $\frac{-3}{2}$.

Final answer:

Hence,  the multiplicative inverse of $\frac{-2}{3}$ is $\frac{-3}{2}$ and

the additive inverse of $\frac{-2}{3}$ is $\frac{2}{3}$

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