**Natural numbers** The counting numbers 1,2,3,4 . . . are called natural numbers.

**Whole number** All natural numbers including zero are called whole numbers.

Properties of whole number:-

**Addition**– closure property- the sum of whole numbers is always a whole number.

Commutative property- a+b = b+a

Associative property- (a+b)+c = a+(b+c)

Identity element- if zero is added to any whole number the sum is the number itself.

0+a = a+0 = a

**subtraction** – closure property- the difference of two whole numbers is not necessary a whole number a-b ≠ b-a not necessary a whole number.

Commutative property a-b ≠ b-a is not defined.

12-4 ≠ 4-12 is not defined.

Property of zero- 0-a ≠ 0-b is not a defined.

Associative property- (a-b)-c ≠ a-(b-c)

**Division**– Dividend- the number which is to be divided is called dividend.

**Divisor**– the number by which dividend is divided is called the divisor.

**Quotient**– the number of times the divisor is contained in the dividend is called the quotient.

**Reminder**– the left over number after division is called the reminder.

Thus, the relationship between these terms.

**Integer** All whole numbers along with negatives of natural numbers are called integers.

**Fractions** The numbers in the form of a/b where a and b are whole numbers and

**Rational numbers** The numbers in the form of a/b a where a and b are integers.

Fractions are also rational numbers a is called numerator and b is called denominator

equivalent rational number .

**Relational numbers between two relational numbers**

If given two relational numbers are a and b then is relational number between a and b.

Example

and

**More that one relational numbers between two rational numbers**

Write and rational numbers between and

Convert two given rational number into equivalent form with common denominator

To obtain 4 Relational numbers between them multiply numerator and denominators with (4+1=5) to make equivalent relational numbers(Multiply n+1 times where n is required number of relational number between two relational number)

and

then

and

**Relational numbers addition and subtraction**

where the denominator of Relational numbers is greater.

**Relational numbers multiplication**

**Relational numbers division**

**Factor**– A factor of a number is an exact divisor of the number. Itself in other word the number that are multiplied to get a product are called the factor . for e.g.- 1,2,3,4,6&12 are the factors of 12.

Multiple- a multiple of a number is a number obtained by multiplying it by a natural number. If we multiply 4 by 1,2,3 we get 4,8, 12 which we all multiple of 4.

**Even number**– A natural number which is exactly divided by 2 is called an even number.

**Odd number**– A natural number which is not exactly divisible by 2 is called an odd number.

**Prime number**– A natural number which is greater than 1 & whose only factors are 1 and the number itself is a prime number.

**Composite number**– The number having more than two factors are called composite numbers.

**Co-prime numbers**– The two numbers which has no common factor other than one are called co-prime number (2,3) (3,4)