### NUMBERS are the basics of math. They form the base and are used in all the math calculations. Types of Numbers are as below

*Natural Numbers**Whole Numbers**Integers**Rational Numbers*

#### Definitions

**Natural Numbers** – These are numbers starting from 1 up infinity i.e 1,2,3,4,……………………Infinity

**Whole Numbers** – These are Natural numbers along with 0 (zero). i.e 0, 1 , 2 ,3, 4,……………………….Infinity

**Integers** – These are positive (+) and Negative (-) whole numbers. i.e -infinity ………..-4, -3 , -2 , -1 , 0 , 1, 2 , 3, 4 ,…………infinity

**Rational numbers** – These are numbers in a/b form i.e 1 / 2 , 3 / 4 ……….. Also, fractions can be expressed as decimal number i.e 0.5(half) = 1/2 (half).

### How to find the Greatest number

**Sol: –** Count the number of digits in each number. The number which has maximum digits is greatest number.

i.e for Ex. we have 55 and 555 . The number of digits in 55 are 2 and number of digits in 555 are 3. hence, 555 is greatest number.

Another ex – 6666, 55555 . In this case, 6666 has 4 digits and 55555 has 5 digits and hence 55555 is greatest number .

Lets see one more example .. 2561, 3561 … Here if we see, the number of digits in both the numbers are 4. Then how to decide?? In such cases we need to study the number

Any number is expressed as in the above sketch. Starting from right every number shall have a units place, tens place, hundreds place, thousands place , ten thousands place, lakhs place , ten lakhs and crores place etc….The number in above sketch is read as 8 crores, 76 lakhs, 54 thousand,3 hundred , 21.

Now lets compare the numbers above 2561 ,3561 … In these numbers, if we see, Thousands digit is 2 in 2561. and Thousands digit is 3 in 3561. As thousands digit 3 is greater than 2 means 3561 is greater than 2561.

#### IMPORTANT ASPECTS TO REMEMBER

*Greatest ———–**Single digit number is 9**Double digit number is 99**Triple digit number is 999**Four digit number is 9999**and so on 99999999999 …………….*

## B O D M A S —- PRINCIPLE

BODMAS RULE IS important to know before doing any addition, multiplication, division or substraction. This principle explains us the order of operations or calculations.

Full form of BODMAS is * B *racket open,

*rder,*

**O***ivision,*

**D***ultiplication,*

**M****ddition,**

*A**ubstraction.*

**S**Lets see an example . we need answer for 3+(6+2)

- First start with bracket and the operation inside the bracket needs to be done first i.e 6+2 = 8 ; and then 3+ 8 = 11. The same can also be written as (3+6) +2 , the answer here also is 9+2 = 11 . This is called as
**Associative property for Addition ——- 1+(2+3) = ( 1+2) +3.**The answer is same . - Now the same rule even applies for multiplication 1x(2×3) = (1×2)x3 = 6. This is
**Associative property for Multiplication.** - Remember the associative property is not possible for
*substraction*and*division*. i.e 1-(2-3) is not equal to (1-2)-3 - Commutative Property for addition ——— 1+2 = 2+1 =3
- Also ,Commutative property for multiplication ——— 1×2 = 2×1 = 2
- For Division and substraction, Commutative property is not applicable
**.** **Distributivity of Multiplication over**–*Addition*

1 x (2+3) = 1 x 5 = 5. The same can also be written as

(1×2) +(1×3) = 2+3 =5

##### Additive and Multiplicative Identity

Any number added to a particular identity, if we get same number then that identity is called additive identity. Example 1 + 0 = 1 ; and we cannot get 1 when 1 is added to any other natural number. Hence, Additive identity for whole numbers is 0 (zero).

Similarly, if any number is multiplied to a particular identity, if we get same number then that identity is called multiplicative identity. Example 1 x 1 = 1 2x 1 = 2; and we cannot get same number when multiplied to any other natural number. Hence, multiplicative identity for whole numbers is 1.

###### To summarise we had learned the following

*Definition of numbers**Finding the greatest number**BODMAS rule**Associative Property**Commutative property**Additive identity**Multiplicative identity*