## Key Concepts

Contents

**Identity Properties****Identity Property of Addition:**For any real number*a*: \(a+0=a\phantom{\rule{1.5em}{0ex}}0+a=a\phantom{\rule{1.5em}{0ex}}\)**0**is the**additive identity****Identity Property of Multiplication:**For any real number*a*: \(a\cdot 1=a\phantom{\rule{1.5em}{0ex}}1\cdot a=a\phantom{\rule{1.5em}{0ex}}\)**1**is the**multiplicative identity**

**Inverse Properties****Inverse Property of Addition:**For any real number*a*: \(a+\left(-a\right)=0\phantom{\rule{1.5em}{0ex}}-a\) is the**additive inverse**of*a***Inverse Property of Multiplication:**For any real number*a*: \(\left(a\ne 0\right)\phantom{\rule{1.5em}{0ex}}a\cdot \frac{1}{a}=1\phantom{\rule{1.5em}{0ex}}\frac{1}{a}\) is the**multiplicative inverse**of*a*

**Properties of Zero****Multiplication by Zero:**For any real number*a*,

\(\begin{array}{} a⋅0=0 & 0⋅a=0 & \text{The product of any number and 0 is 0.}\end{array}\)**Division of Zero:**For any real number*a*,

\(\begin{array}{} \frac{0}{a}=0 & 0+a=0 & \text{Zero divided by any real number, except itself, is zero.}\end{array}\)**Division by Zero:**For any real number*a,*\(\frac{0}{a}\) is undefined and \(a÷0\) 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 \(\frac{1}{a}\).