Question

The numbers ______ and _____ are their own reciprocals.

Answer 1

The 1 and -1 are the numbers having their own reciprocal.

Solution:

As we all know that no rational number will give one (1) if it is multiplied with zero. And there is no reciprocal for the rational number zero and also it has not having any multiplicative inverse.

The 1 and -1 are the two numbers which having reciprocal of its own. Except 1 and -1 no other numbers are not having its own reciprocal.

Ifx=1, then the reciprocal $\frac{1}{x}$ $=\frac{1}{1}$ =1

Ifx=-1, then the reciprocal $\frac{1}{x}$ $=\frac{1}{-1}$  =-1

Therefore, the reciprocal of 1 and -1 is 1 and -1.

Answer 2

Answer:

The numbers 1 and -1 are their own reciprocals.

Step-by-step explanation:

The numbers 1 and -1 are their own reciprocals.

$1 \times \frac{1}{1} = 1$

$-1 \times \frac{1}{(-1)} = 1$

$If \: a \:is\: any \:real\: number ,\: a≠0 , \\\:a\: \times \frac{1}{a} = 1 = \frac{1}{a}\times a\\ \: a\: is \\\:multiplicative \:inverse \:of\: \frac{1}{a} \: or \:vice \:versa$

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