# Algebra Properties

> A short look at some important algebra properties and their formulas

- Canonical: https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula
- Published: 2020-06-21
- Updated: 2020-06-21

## Resources

1. [Deriving the Quadratic Formula](https://www.chilimath.com/lessons/intermediate-algebra/derive-quadratic-formula/)

## Properties of Algebra

### Commutative Property of Algebra

Definition:

1. involving the condition that a group of quantities connected by operators gives the same result whatever the order of the quantities involved, e.g. a × b = b × a.
2. relating to or involving substitution or exchange.

_[Interactive BlockMath: view it at https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula]_
_[Interactive BlockMath: view it at https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula]_
### Associativity Property of Algebra

Grouping of more than two numbers to perform basic arithmetic operations of addition/multiplication does not affect the final result.

_[Interactive BlockMath: view it at https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula]_
_[Interactive BlockMath: view it at https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula]_
### Distributive Property of Algebra

The distributive property defines that the product of a single term and a sum or difference of two or more terms inside the bracket is same as multiplying each addend by the single term and then adding or subtracting the products.

_[Interactive BlockMath: view it at https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula]_
_[Interactive BlockMath: view it at https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula]_
### Additive Identity Property

_[Interactive BlockMath: view it at https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula]_
### Multiplicative Identity Property

_[Interactive BlockMath: view it at https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula]_
### Additive Inverse Property

_[Interactive BlockMath: view it at https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula]_
### Multiplicative Inverse Property

_[Interactive BlockMath: view it at https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula]_
## Logarithmic Properties

### Product Rule

The log of a product is equal to the sum of the log of the first base and the log of the second base:

_[Interactive BlockMath: view it at https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula]_
### Quotient Rule

The log of a quotient is equal to the difference of the logs of the numerator and denominator:

_[Interactive BlockMath: view it at https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula]_
### Power Rule

The log of a power is equal to the power times the log of the base:

_[Interactive BlockMath: view it at https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula]_
### Change of Base Formula

The log of a new base is the log of the new base divided by the log of the old base in the new base:

_[Interactive BlockMath: view it at https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula]_
### Base Switch Rule

_[Interactive BlockMath: view it at https://dennisokeeffe.com/blog/2020-06-21-deriving-the-quadratic-formula]_