Question

multiplicative inverse of a negative rational number is​

Answer 1

Multiplicative inverse of a negative rational number is also a negative rational number.

Concept:

Two non-zero rational numbers are said to be multiplicative inverse of each other, if their product is 1,

that is, $a\times b=1$

Further we can compute, $b=\dfrac{1}{a}$

This states that if a number is $a$, then $\dfrac{1}{a}$ is its multiplicative inverse.

Step-by-step explanation:

Let, $(-\dfrac{a}{b})$ be a negative rational number, where both a and b are positive integers with b being non-zero.

Then its multiplicative inverse is

$1\div(-\dfrac{a}{b})$

= $1\times (-\dfrac{b}{a})$

= $-\dfrac{b}{a}$

which is also a negative rational number.

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