Question

Why is the product of negative reciprocals always -1?

Answer 1

Answer:

please check the explanation.

Step-by-step explanation:

Let suppose we have a number = n  

• n≠0    

The negative reciprocal of 'n' = -1/n

Taking the product of 'n' and its negative reciprocal '-1/n':

$n\left(-\frac{1}{n}\right)$

remove parentheses: (-a) = -a

$=-n\frac{1}{n}$

$\mathrm{Multiply\:fractions}:\quad \:a\times \frac{b}{c}=\frac{a\:\times \:b}{c}$

$=-\frac{1\times \:n}{n}$

$\mathrm{Cancel\:the\:common\:factor:}\:n$

$=-1$

Canceling the common factor (the number itself) will bring -1.

It proves that the multiplication of any number and its negative reciprocal will always yield -1.