Question

What is the opposite and reciprocal of -1?

Answer 1

Hint: Now we know that the opposite of a number is a number which upon adding to the given number gives 0. Similarly reciprocal of the number is a number which upon multiplying to the given number gives the product as 1. Hence using this we will easily find the value of opposite and reciprocal.

Complete step by step solution:
Let us first understand the concept of additive identity and multiplicative identity.
The additive identity is a number which upon adding to any number gives the same number.
Hence additive identity is nothing but 0 in case of real numbers. Since we have for any number x $x+0=x$ .
Now similarly multiplicative identity is a number which upon multiplying to any number gives the product as the same number. Hence we get the multiplicative identity of real numbers is 1 as we have for any real number y $y\times 1=y$.
Now opposite of a number is nothing but a number which upon adding gives us additive identity.
Hence the opposite of -1 must be +1 as we have $-1+1=0$
Similarly reciprocal of a number is a number which upon multiplying to the number is given multiplicative identity.
Hence reciprocal of -1 is -1 as $-1\times -1=1$
Hence the opposite of -1 is 1 and the reciprocal of -1 is -1.

Note: Now note that opposite of any number is nothing but the -1 times the number. Similarly reciprocal of any number x is nothing but $\dfrac{1}{x}$ . This is because we have $x+\left( -1 \right)\left( x \right)=0$ and $x\times \dfrac{1}{x}=1$ . Also note that we cannot find the reciprocal of 0.