# What is the opposite and reciprocal of 2 3/4?

Jul 9, 2015

The opposite (additive inverse) of $2 \frac{3}{4} = \frac{11}{4}$ is $- 2 \frac{3}{4} = - \frac{11}{4}$

The reciprocal (multiplicative inverse) of $2 \frac{3}{4} = \frac{11}{4}$ is $\frac{4}{11}$.

#### Explanation:

The additive identity is $0$. This has the property that for any number $a$:

$a + 0 = 0 + a = a$

If $a$ is any number, then $- a$ is called the opposite or additive inverse of $a$. It has the property that:

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

The additive inverse of $2 \frac{3}{4} = \frac{11}{4}$ is $- 2 \frac{3}{4} = - \frac{11}{4}$

Multiplication

The multiplicative identity is $1$. This has the property that for any number $a$:

$a \cdot 1 = 1 \cdot a = a$

If $a$ is any non-zero number, then $\frac{1}{a}$ is called the reciprocal or multiplicative inverse of $a$. It has the property that:

$a \cdot \left(\frac{1}{a}\right) = \left(\frac{1}{a}\right) \cdot a = 1$

The multiplicative inverse of $2 \frac{3}{4} = \frac{11}{4}$ is $\frac{1}{\frac{11}{4}} = \frac{4}{11}$.