# What is the opposite and reciprocal of 1?

Jun 25, 2015

The opposite and reciprocal of 1 is $- \frac{1}{1}$, which is just -1.

Jun 25, 2015

The opposite of $1$ is $- 1$ and
the reciprocal of $1$ is $1$.
The opposite (also known as the additive inverse) is the number we have to add to get an answer equal to the additive identity, $0$. Since $1 + \left(- 1\right) = \left(- 1\right) + 1 = 0$, the opposite of $1$ is $- 1$.
The reciprocal (also known as the multiplicative inverse) is the number we have to multiply to get an answer equal to the multiplicative identity, $1$. Since $1 \times 1 = 1$, the reciprocal of $1$ is $1$.
(The only numbers that are their own reciprocals are $1$ and $- 1$.)