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galina1969 [7]
3 years ago
9

Why is the product of negative reciprocals always -1?

Mathematics
1 answer:
erik [133]3 years ago
3 0

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.

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