Key Concepts

• Identity Properties
  • Identity Property of Addition:
    For any real number $a$: $a+0=a(0)+a=a$.  $0$ is the additive identity
  • Identity Property of Multiplication:
    For any real number $a$:
    • $a\cdot 1=a$
    • $1\cdot a=a$
    • $1$ is the multiplicative identity
• Inverse Properties
  • Inverse Property of Addition: For any real number $a$: $a+\left(-a\right)=0-a$ is the additive inverse of $a$
  • Inverse Property of Multiplication: For any real number $a$: $\left(a\ne 0\right)a\cdot {\Large\frac{1}{a}}=1$.   The multiplicative inverse of $a$ is ${\Large\frac{1}{a}}$.
• Properties of Zero
  • Multiplication by Zero: For any real number $a$,
    $\begin{array}{ccccccc}\hfill a\cdot 0=0\hfill & & & \hfill 0\cdot a=0\hfill & & & \hfill \text{The product of any number and 0 is 0.}\hfill \end{array}$
  • Division of Zero: For any real number $a$,
    $\begin{array}{ccccccc}\hfill {\Large\frac{0}{a}}=0\hfill & & & \hfill 0+a=0\hfill & & & \hfill \text{Zero divided by any real number, except itself, is zero.}\hfill \end{array}$
  • Division by Zero: For any real number $a$, ${\Large\frac{0}{a}}$ is undefined and $a\div 0$ is undefined. Division by zero is undefined.

Glossary

Additive Identity

The additive identity is $0$. When zero is added to any number, it does not change the value.

Additive Inverse

The opposite of a number is its additive inverse. The additive inverse of a is $-a$ .

Multiplicative Identity

The multiplicative identity is $1$. When one multiplies any number, it does not change the value.

Multiplicative Inverse

The reciprocal of a number is its multiplicative inverse. The multiplicative inverse of $a$ is ${\Large\frac{1}{a}}$ .