# What is the opposite and reciprocal of -4?

May 4, 2018

The opposite is the negation, $- \left(- 4\right) = 4$.

The reciprocal is $\frac{1}{- 4} = - \frac{1}{4}$

May 4, 2018

$4 \text{ and } - \frac{1}{4}$

#### Explanation:

$\text{the opposite of a number is the negative of the number}$

$\Rightarrow \text{opposite of "-4" is } - \left(- 4\right) = 4$

$\text{the reciprocal of any number n is } \frac{1}{n}$

$\Rightarrow \text{reciprocal of "-4" is } \frac{1}{- 4} = - \frac{1}{4}$

May 4, 2018

The additive inverse of $- 4$ is $+ 4$

The reciprocal of $- 4$ is $- \frac{1}{4}$

#### Explanation:

There are two types of 'opposites':

Opposites for adding and opposites for multiplying.

Their sum is always $0$.

$\left(- 3\right) + \left(+ 3\right) = 0$

$\left(+ 15\right) + \left(- 15\right) = 0$

They have the same value but opposite signs,

Multiplying opposites are known as "multiplicative inverses"
which are also known as "reciprocals'.

Their product is always $1$

$\frac{2}{3} \times \frac{3}{2} = 1$

$- \frac{5}{2} \times - \frac{2}{5} = 1$

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

(The number is inverted to find its reciprocal)