"Whole Numbers"

Introduction:
Whole numbers are the ordinary numbers including zero i.e, they are actually 0,1,2,3,........
Place Values:
The place value of a any whole number matters.For example;the place value of 2 in 24 is different then the place value of 2 in 204 or the place value of 2 in 002.

The table for the place value is as follows:
Placevalue Name of Position
1 000 Ones position (usually called unit)
1 000 Tens
1 000 Hundreds
1 000 Thousands
1 000 000 Ten thousands
1 000 000 Hundred Thousands
1 000 000 Millions
1 000 000 000 Ten Millions
1 000 000 000 Hundred millions
1 000 000 000 Billions

Example:
For example we can write each digit of 23478,according to its values as:
23478=20000+3000+400+70+8
The symbol "=" used here is called the equality sign,other symblos used with the whole numbers are ">" and "<" ,called "graeter than" and "less than" signs respectively.they are used as ,
34 "is greater than" 28 can be written as;
34 > 28
Similarly,24 "is less than" 67 can be written as;
24 < 67

Properties:

1) Closure Property:
Whole numbers obey the closure property with respect to both addition and multiplication.
Example:
2 + 3 = 5
Here 2 & 3 are two whole numbers and their sum 5 is also a whole number.
3 ´ 4 = 12
Again,3 & 4 are whole numbers and their porduct 12 is also a whole number.

2) Commutative Property.
Whole numbers are also commutative i.e,when their positions are swiched the result remains the same.This property holds both for multiplication and addition.
Example:
2 + 4 = 4 + 2
3 * 4 = 4 * 3

3) Associative property.
The assosiative property both for addition and multiplication is as follows,
Example:
2 + (3 + 5) = ( 2 + 3) + 5
2 * (3 * 5) = (2 * 3) * 5

4) Distributive Property.
The distributive property of addition over multiplication is explained with example as follows,
Example:
10 * (3 + 4) = (10 * 3) + (10 * 4)

5) The Additive Property.
This property says that if you add 0 to any number the number remains the same.So the 0 is called additive property.
Example:
2 + 0 = 0 + 2 = 2

6) The Multiplicative Property.
This property says that if you multiply 1 with any whole number the number remains the same.
Example:
7 * 1 = 7 * 1 = 7

Operations.
While performing different operations on whole numbers we have to follow a proper sequence of operations.These operations may be Addition,Subtraction,Mutiplication And Division.

This sequence or order of operations if as follows:
a) Multiply and divide, whichever comes first, from left to right.
b) Add and subtract, whichever comes first, from left to right.

Example:
1 + 20 * 8 ÷ 2 =
1 + 160 ÷ 2 =
1 + 80 =
81.
Now what if we want to add 1 to 20 first and want to do the remaining operations later?For this we use "Brackets".We solve the Brackets first.
Example:
2 * (3 + 4) =
2 * 7 =
14.

 

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