# Here are some of the basic rules and vocabulary of Algebra.

## 2.  Opposite – Another name for the opposite of a number is the additive inverse.      $\left&space;[&space;a\mid&space;-a&space;\right&space;]$

$a&space;+&space;(-a)=&space;0$

remove the brackets

$a&space;-a&space;=&space;0$

## 3.  Reciprocal – Another name for the reciprocal of a number is the multiplicative inverse.  $\left&space;[&space;a\mid&space;\frac{1}{a}\right&space;]$

$a*\frac{1}{a}=&space;1$

## 4.  Fractions - A fraction has both a denominator and a numerator.

$\frac{a}{b}=\frac{Numerator}{Denominator}$

## 5.  Properties of Operations

### I like to think of the word order when I think of this property.  Almost every day we commute to school or to work.  We leave home and go to school in the morning.  At the end of the day we leave school and go home.  The order changes but the route remains relatively the same.  When we add or multiply the result is the same no matter what order the terms are in.

$a+b=b+a$

$a*b=b*a$

### What group or association do you belong to?  Are you a member of the Red Cross or the Red Crescent Society?  In this property the groups are changed but the end result is the same.

$\left&space;(a+b&space;\right&space;)+c=a&space;+&space;\left&space;(&space;b+c&space;\right&space;)$

$\left&space;(a*b&space;\right&space;)*c=a&space;*&space;\left&space;(&space;b*c&space;\right&space;)$

### In the property the number in front of a group of addition is distributed over all the terms of the addition.  In other words multiply each term inside the brackets by the number in front of the bracket.

$a*\left&space;(&space;b+c&space;\right&space;)=&space;a*b&space;+&space;a*c$

### The quantity zero [0] is the identity element of addition.  When you add 0 to any number you end up the identical number you started with.

$a+0=a$

### The quantity one [1] is the identity element of multiplication.  When you multiply any number by 1 you end up with the identical number.

$a*1=a$

### The additive inverse of a number is called the opposite of the number.  If you add a number and its additive inverse the result is equal to 0.

$a+\left&space;(&space;-a&space;\right&space;)=0$

### The multiplicative inverse of a number is called the reciprocal of the number.  If you multiply a number by its multiplicative inverse the result is equal to 1.

$a*\frac{1}{a}=&space;1$

## 6.  Rules for Adding Terms

### $\left&space;(&space;+,+&space;\right&space;)\overset{add}{\rightarrow}+$

$\left&space;(&space;-,-\right&space;)\overset{add}{\rightarrow}-$

### $\left&space;(&space;\left&space;(&space;+&space;\right&space;),-\right&space;)\overset{subract}{\rightarrow}+$

$\left&space;(&space;\left&space;(&space;-&space;\right&space;),+\right&space;)\overset{subract}{\rightarrow}-$

## 7.  Rules for Multiplication

### $\left&space;(&space;+*+&space;\right&space;)=+$

$\left&space;(&space;-*-\right&space;)=+$

### $\left&space;(&space;+*-\right&space;)=-$

$\left&space;(&space;-*+\right&space;)=-$

## 8.  More Vocabulary

### $24=1*24=1*\left&space;(&space;2*12&space;\right&space;)=1*2*\left&space;(&space;2*6&space;\right&space;)=1*2*2*\left&space;(&space;2*3&space;\right&space;)=1*2*2*2*3$

Filed under: Pre-requisites for Pre-Calculus

Like this post? Subscribe to my RSS feed and get loads more!