Algebra is the language of Mathematics. Signed Numbers is the language of Algebra. To Learn Algebra The Easy Way is to first Master or become very Proficient in the Operations of: ADDITION, SUBTRACTION, MULTIPLICATION and DIVISION of NEGATIVE and POSTIVE NUMBERS, and Know the ORDER in which these OPERATIONS must be Performed.

### Step 1

To begin the study of positive and negative Numbers, which are also called the 'signed numbers', one needs to become very familiar with the Number Line, the different SETS of NUMBERS, and their Postions or Order on the Number Line. Please click on the Image to the left to get a better view of the Number Line.

### Step 2

The SET of NATURAL NUMBERS, also called the SET of COUNTING NUMBERS, is of the form, N = { 1,2,3,4,5,... }. The three dots after the number 5 signifies that the numbers continue in the same manner, Infinitely. To see the Graph of the SET of NATURAL NUMBERS on the NUMBER LINE, please click on the Image on the left.

### Step 3

The SET of WHOLE NUMBERS is of the form, W = { 0,1,2,3,4,5,... }. The difference between the SET of NATURAL NUMBERS and the Set of WHOLE NUMBERS, is that the set of WHOLE NUMBERS contains the Element ZERO ( 0 ). The SET of NATURAL NUMBERS does not contain the element zero. Please click on the Image on the left to see the graph of the SET of WHOLE NUMBERS.

### Step 4

The SET of NUMBERS that are called the INTERGERS is of the form, Z = { ...,-4,-3,-2,-1,0,1,2,3,4,... }. ZERO ( 0 ), is the Mid-point of the NUMBER LINE. The SET of NATURAL NUMBERS is to the Right side of ZERO and are called the Positive Numbers. The Sign for the Positive Numbers is the Plus ( + ) sign . The Numbers to the Left of ZERO are Opposite to the SET of NATURAL NUMBERS and are called the Negative Numbers. The Sign used is the Minus ( - ) sign. The Union of the Negative and Positive Numbers with the number Zero makes up the SET of INTERGERS. Since ZERO ( 0 ) is neither to the Left side or Right side of ZERO then the Number Zero is neither a Positive or a Negative Number. Please click on the Image to the left to see the graph of the SET of INTERGERS.

### Step 5

The SET of RATIONAL NUMBERS, is the Set that contains all the numbers that are the Ratios of two Integers, that is if U is an Integer and V is an Integer, the Number ( U/V ) where V is not equal to Zero is called a rational number. Some examples of Rational Numbers are: ( 1/2 ), ( 5/6 ), ( 3/4 ),( -3/4 ), ( .3 ), ( 7 ). The reason why ( 7 ) is considered to be a rational number is because ( 7 ) is understood to be divided by ( 1 ), that is ( 7/1 ). All integers are Rational Numbers since any integer including zero is understood to be divided by the number one ( 1 ). The SET of Rational Numbers is of the form, Q = { ... -4 , -3.6 , -3/2 , -3 , -2 , -1 , -3/4 , -1/4 , 0 , 1/5 , 1... }. Please note that almost every point on the number line is a rational numbers, except for some points which are called irrational numbers. Please click on the Image for some examples of Rational Numbers.

### Step 6

The IRRATIONAL NUMBERS are non-repeating, non-terminating decimals. For example, the following decimals are irrational numbers: ( 0.1112131415...), pi = 3.14159..., e = 2.71828..., the square roots of non-perfect square numbers such as ( 2 ), ( 3 ), ( 5 ) etc.. Please click the image on the left.

### Step 7

The REAL NUMBERS is the Set of the Union of the Rational Numbers and the Irrational Numbers. Please click the image to see the graph of REAL NUMBERS.