# Definition of Natural Number and property, example, Sum part-1

## Definition of Natural Number

The definition of natural number is hidden in its name itself. how?

The number that is used in counting natural things. These are called natural numbers.

It is also called counting numbers. Because this number is used to count anything.

Natural numbers are positive integers. The values of integer numbers range from – ∞ to + ∞. One part of which is a positive integer and the other negative integer. A positive integer is a natural number.

## Natural number value

The value of a natural number varies from 1 to ∞.

Ex – 1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 ……… ∞

## Natural Numbers Examples

Find the number of pens shown in the above picture.
To find the number of pens present in this picture, we will start counting the pens from one end.

Let’s start counting the pen from right to left.

Thus the first red pen, Second blue pen, Third green pen, Fourth yellow pen, Fifth orang pen, Sixth black pen

An object is started to be counted by one. No to zero. This proves it. Of zero is not a natural number.

We started counting pens from one to six. So the number of pens is six.

## Property of Natural Number

1. Closure Property
2. Associative Property
3. Commutative Property
4. Distributive Property

### Closure Property

Adding and multiplying any two or more natural numbers gives a natural number.

The sum of two natural numbers is a natural number.

ex – 2+2 = 4. 5+3 = 8, 9+2 = 11

#### Multiplication

The result of two natural numbers is a natural number.

Ex – 2×4 = 12, 5×8 = 40, 7×3 = 21

#### Subtraction

The subtraction of two natural numbers may or may not be a natural number. If the smaller natural numbers are subtracted from the larger natural numbers, then the obtained numbers will be natural numbers.

Conversely, if the larger natural number is subtracted from the smaller natural number, then the number obtained will not be a natural number.

Ex 5 – 3 = 2, 7 -10 = -3

## Division

The quotient of two natural numbers may or may not be a natural number.

Ex – 10/8 = 1.25, 10/5 = 2

### Associative Property

Associative property of natural number is correct in case of addition and multiplication.

a + ( b + c ) = ( a + b ) + c

#### Multiplication

a × ( b × c ) = ( a × b ) × c

Associative property of natural number is not correct in the case of Subtraction and Division.

#### Subtraction

a – ( b – c ) ≠ ( a – b ) – c

#### Division

a ÷ ( b ÷ c ) ≠ ( a ÷ b ) ÷ c

### Commutative Property

Commutative Property of natural number is correct in case of addition and multiplication

Ex – x + y = y + x and a × b = b × a.

Commutative Property of natural number is not correct in case of addition and multiplication.

x – y ≠ y – x and x ÷ y ≠ y ÷ x.

### Distributive Property

Distributive Property of natural number is correct in case of addition and multiplication

a × (b + c) = ab + ac

Distributive Property of natural number is not correct in case of addition and multiplication.

a × (b – c) = ab – ac.

## Natural Numbers from 1 to 100

Which natural number has no successor?

No!
There is no natural number that has no successor. All-natural numbers have successors.

Which natural number has no predecessor?

No!
There is no natural number that has no predecessor. All-natural numbers have a predecessor.

Who invented natural numbers?

Natural numbers always existed. But we started studying it seriously since the time of Greek philosophers, Pythagoras and Archimedes.

What is the smallest natural number?

1 is the smallest natural number.

What is the natural number with an example?

1, 2, 3, 4, 5, 6, 7, 8, 9 …….

What is the natural number definition?

The numbers that are used to count natural objects. It is called a natural number.

What is the natural number symbol?

The natural number is represented by “N“.

which natural number is nearest to 8485?

8484 and 8486

Which natural number is equal to its cube?

27 is a cube of 3. 8 is a cube of 2. 64 is a cube of 4 etc.

Are natural numbers negative?

No!
Natural numbers are only positive.

Are natural numbers rational?

No!
Because an object cannot be counted in p / q. Can we tell a pen that the number of pens is 2/5. No no When counting an item, it is considered to be the same.

Are natural numbers whole numbers?

All whole numbers are natural numbers except zero.

Are natural numbers countable?

Yes

Are natural numbers real numbers?

Yes

Can a natural number be decimal?

No

Can Natural Numbers be Rational?

No

Can a natural number be decimal?

No

A natural number is also known as

counting numbers

Natural number to 10.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

What is the sum of natural numbers from 1 to 100?

5050

Three natural numbers after 1500

Ans – 1501, 1502, 1503

All Trigonometry Formulas For Class 10, 11, 12 (PDF)