Question

The multiplicative inverse of a negative rational number is:
A. a positive rational number
B. a negative rational number
C. 0
D. 1

Answer 1

Hint:In order to this question, to know the exact option for the multiplicative inverse of a negative rational number, we will explain it theoretically first and then give an example to understand how the multiplicative inverse of a negative rational number is a reciprocal of the same given negative rational number.

Complete step by step answer:
The multiplicative inverse of a negative number must also be a negative number. The product of a number and its multiplicative inverse is (positive) 1, which cannot be obtained by multiplying two positive numbers together.The reciprocal of a particular number is also known as the multiplicative inverse.

With the exception of zero, which is equal to zero when multiplied by zero, all real numbers have reciprocals. A negative number multiplied by its counterpart (which is likewise a negative number) produces a positive number.The reciprocal of a number expresses the inverse property of multiplication. For the variable a it can be written as:
$ax.\dfrac{1}{a} = \dfrac{1}{a}x.a = 1,\,a \ne 0 \\
\Rightarrow - ax. - \dfrac{1}{a} = - \dfrac{1}{a}x. - a,\,a \ne 0 \\ $
Multiplication is used to define division. In truth, division is the same as multiplying a given integer by its reciprocal or multiplicative inverse. As a result, division and multiplication are regarded as inverse operations, just as addition and subtraction are regarded as inverse operations. If a number $x$ is multiplied by a number $y$ , the resultant must be divided by $y - $ or multiplied by $1 \ne y$ to return to the original number $x$ . This shows how x and its counterpart $1 \ne x$ have a multiplicative inverse relationship.

Hence, the correct option is B.

Note:$\dfrac{1}{N}$ or ${N^{ - 1}}$ is the multiplicative inverse of a number, such as $N$ . It's also known as reciprocal, which comes from the Latin word reciprocus. The word inverse refers to something that is the polar opposite of anything else. The reciprocal of a number obtained is one whose value equals identity 1 when multiplied by the original number.