Question

What is the opposite and reciprocal of \[1\] \[?\]

Answer 1

Hint: To find the opposite of a given number, we need to find the additive inverse of the given number. Additive inverse of a given number is a number which when added with the given number gives \[0\]. Also, to find the reciprocal of the given number, we need to find the multiplicative inverse of the given number. Multiplicative inverse of a given number is a number which when multiplied with the given number gives \[1\].

Complete step by step answer:
Since the opposite of \[1\] is a number which when added with \[1\] gives \[0\]. Suppose \[x\] be the opposite number of \[1\], then
\[x + 1 = 0\]
\[ \Rightarrow x = - 1\]
Hence, the opposite of \[1\] is −1.
Also, the reciprocal of \[1\] is a number which when multiplied with \[1\] gives \[1\]. Suppose \[y\] be the reciprocal number of \[1\], then
\[y \times 1 = 1\]
\[ \Rightarrow y = 1\]
Hence, the reciprocal of \[1\] is \[1\].

Note:
Note that the reciprocal of the given number exists if and only if the given number must be a nonzero number. Also note that to solve this type of questions we must have knowledge of additive inverse and multiplicative inverse laws (\[0\] is an additive identity element and \[1\] is the multiplicative identity element). The reciprocal of a reciprocal of the given number gives back the given number.