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# Elementary Mathematics for Children

__Introduction__

This hub focused on a particular topic, that to understand the basic number system and basic operations in Mathematics. Generally Mathematics is the branch of a particular discipline or science which is essential to support all other branches of knowledge like Economics, Computer, Physics…. . Unfortunately some of the people facing many difficulties to grasp the different concepts of Mathematics. Here the problem is the lacking of effective understanding of basics of Mathematics. By this hub you can understand the basis of Mathematics including number system and the basic operations ( adding, subtraction, multiplication, division )

__Number system__

When we heard ‘Mathematics’, obviously we think about numbers. For simplicity we can categorize number system in to six like listed below.

1) __Natural Numbers (N)__

Natural Numbers can be represented by the letter ‘N’. which contain all the numbers, we used to count like 1,2,3,….

2) __Whole Numbers (W)__

Whole Numbers can be represented by the letter ‘W’. when we add Zero with the natural numbers, we can derive whole numbers. Simply whole numbers are 0,1,2,3,…..

3) __Integer Number (Z)__

Integers are numbers which can represented with the letter ‘Z’. when we put negative numbers with the whole numbers, we can derive Integers

That is ; -3,-2,-1,0,1,2,3

4) __Rational Numbers (Q)__

Rational numbers can be denoted by the letter ‘Q’. actually it is a order of integers, but fractions are included

That is : ….-2,-1.9,-1.8…..-1.1…,-1…….0,……1,…..1.9,..,2,…….

5) __Real Numbers (R )__

Real numbers can be represented with ‘R’ and it contains both Rational and irrational numbers.

6) __Complex Numbers __

Complex number is a difficult concept, so their value will be an imaginary one. for example: Root of - 2

__Basic Operations__

Generally there are four major operations like addition, subtraction, multiplication, division. Each of them are briefly represented with the help of pictures.

__Addition__

addition is the major operation in mathematics . the rules for addition is explained in the following picture.

**Substraction**

Substraction is also another important operation in Mathematics. the rules for subtraction is represented in the following picture

**Multiplication**

The rules for multiplication is pictorially represented given below.

**Division**

Division is another important operation in Mathematics. The rules for the division is explained in the following picture.

__Commutativity__

Commutativity is a concept, which says the importance of order of two numbers. When we interchange the position of two numbers in a equation simultaneously, it will never effect in the result, both in the case of addition and multiplication. So, addition and multiplication of two numbers are commutative.

__Addition :__

2 + 3 = 5

Change order 3 + 2 = 5

__Multiplication :__

2 * 3 = 6

Change order 3 * 2 = 6

But in the case of subtraction and division are not commutative. Because when we interchange the position of two numbers it will provide a different result.

__Substation :__

2 - 3 = -1

Change order 3 - 2 = 1

__Division :__

2 / 3 = 0.66….

Change order 3 / 2 = 1.5

__Associative__

Associative is a concept which says about the importance of the order of three numbers. It also explains, when we interchange order of three numbers in equation it will never alter the result both in the case of addition and multiplication. So, addition and multiplication are associative.

__Addition :__

(2 + 4) + 6 = 12

Change order 2 + (4 +6 ) = 12

__Multiplication__

(2 * 4) * 6 = 48

Change order 2 * (4 * 6) = 48

But in the case of subtraction and division are not associative. The reason is that when we interchange the order of the equation it will change the result.

__Subtraction :__

(2 – 4) – 6 = -8

Change order 2 – (4 – 6) = 4

__Division :__

(2 / 4) / 6 = 0.083

Change order 2 / ( 4/ 6) = 3