Whole Numbers Definition, Property, Example Part-2

Whole Numbers Definition

If zero is also included in the natural number( 1, 2, 3, 4, 5, 6, 7 …. ∞ ), then those numbers are Whole numbers.ex – 0, 1, 2, 3, 4, 5, 6, 7, 8 ……. ∞

If W is removed from the word whole, the word becomes a hole word. And we know. That the hole size looks like zero. So from the hole, we will remember zero. Numbers from 0 to infinity are called hole numbers.

Whole Numbers Examples

555, 687, 999, 0, 1800, 1520, 888 etc.

The predecessor of the whole number

The predecessor of the whole number is that number. Which comes 1 digit before the given number. That is, 1 is subtracted from that number to find the predecessor of a whole number.

Ex – What will be the predecessor of 555?

We know To find the predecessor of any number, one is subtracted from that number. Hence the predecessor of 555 is (555-1) = 554.

What will be the predecessor of 2?

Ans – (2-1) = 1

Subtract one of them to find the predecessor of two.

The successor of the whole number

The successor of a whole number is that number. Which comes after 1 digit of the given number. Or to find the successor of a hole number, one is added to that number.

Ex – What will be the successor of 15?

Ans – To find the successor of 15 can be obtained by adding a digit to it. 15 + 1 = 16

What will be the successor of 120?

120+1 = 121

Property of Whole Numbers

Closure Property

If two whole numbers are multiplied and added. So the number received is the whole number. On the other hand, if two whole numbers are divided and subtracted, the number obtained may or may not be a whole number.

The sum of two whole numbers is the whole number.

Whole Number + Whole Number = Whole Number

Ex – 2+2 = 4, 0+1 = 1, 5+8 = 13

Multiplication

Multiplication of two whole numbers is obtained as a whole number.

Whole Number × Whole Number = Whole Number

Ex – 2×2 = 4 , 5×8 = 40, 12×2 = 24

Subtraction

If the smaller whole number is subtracted from the larger whole number then the number obtained will be the whole number. Conversely, if the whole number is subtracted from the smaller whole number, the number received will not be the whole number.

Whole Number “x” – Whole Number “y” = Whole Number ( x>y)

Ex: 4 – 2 = 2, 10 – 5 = 5, 110 – 20 = 90, 999 – 111 = 888

Whole Number “x” – Whole Number ‘y” = Whole Number (x=y)

Ex: 4 – 4 = 0, 15 – 15 = 0, 50 – 50 = 0, 80 – 80 = 0

Whole Number “x” – Whole Number “y” = integer ( x<y)

Ex: 15 – 20 = -5, 40 – 50 = -10, 130 – 140 = -10

Division

The division of two whole numbers will be the whole number only if the dividend is completely divisible by the divisor.

In the above situation, only the whole number can be obtained in case of division. If the quotient is the point or negative. So the whole number will not be received.

Commutative Property

The whole number follows the Commutative Property in addition and multiplication. On the contrary, it does or may not follow.

Two whole numbers can be added in any case, the whole number is obtained. According to the Whole Numbers Definition, these numbers range from zero to infinity

Whole Number “a” + whole Number “b” = Whole Number “b” + Whole Number “a”

a + b = b + a

Ex: 5 + 4 = 4 + 5 In this case, if 5 and 4 are added or 4 and 5 are added, the same answer will come in the two cases.

Multiplication

According to the Whole Numbers Definition, these numbers range from zero to infinity

Whole Number “a” x whole Number “b” = Whole Number “b” x Whole Number “a”

a x b = b x a

Ex: 5 x 4 = 4 x 5| In this case, if 5 and 4 or 4 and 5 are multiplied, the same answer will be given in two cases.

Subtraction

The whole number does not follow the Commutative Property in case of subtraction.

Ex: a – b ≠ b -a

Division

In the case of division, the whole number does not follow the Commutative Property.

Associative Property

If three whole numbers are added or reduced in any case, then, in that case, the whole number is obtained. The whole number in addition and subtraction follows the Associative Property.

In the case of Yoga, the Whole Number follows the Associative Property.

Ex: (a + b) + c = a + (b + c)

Multiplication

In the case of multiplication, the Whole Number follows the Associative Property.

Ex: (a x b) x c = a x (b x c)

Subtraction

In the event of subtraction, the Whole number does not follow the Associative Property.

( a – b ) – c ≠ a – ( b – c )

Division

The whole number does not follow the Associative Property in the position of the part.

Distributive Property

In the case of addition and multiplication, the Whole number follows the Distributive Property.

FAQ

Is 10 a whole number?

True

Is 9 a whole number?

True

What are the first 5 whole numbers?

0, 1, 2, 3, 4

Is seven a whole number?

True

Is 18 a whole number?

True

Is 100 a whole number?

True

Is 13 a whole number?

True

What is a whole number between 1 and 20?

2, 3, 4,5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19

Is 0 a whole number?

Zero is a whole number. It is neither positive nor negative integer. This is the link between Positive and Negative.

Can whole numbers be negative?

No

What are the properties of whole numbers?

The whole number has four properties. 1 – Closure Property, 2 – Commutative Property, 3 – Associative Property, 4 – Distributive Property

Are whole numbers closed under subtraction?

Ans – The whole number is closed under the Subtraction.

Are whole numbers closed under addition?

Ans – The whole number is closed under the Subtraction.

Are whole numbers also natural numbers?

All whole numbers except zero are natural numbers. All-natural numbers are whole numbers. But not all whole numbers are natural numbers.

Are whole numbers rational numbers?

According to the Whole Numbers Definition, these numbers range from zero to infinity. Every whole number can be written in a rational number.

Are whole numbers closed under multiplication?

Yes

Are whole numbers associative under subtraction?

The subtraction of whole numbers is not associative

Which the whole number has no predecessor?

According to the Whole Numbers Definition. The whole zero (0) has no predecessor.

Which of the whole number is not a natural number?

According to the Whole Numbers Definition. Zero (0) is not a natural number.

Which the whole number doesn’t have a successor?

All whole numbers have successors.

Which the whole number is not a rational number?

According to the Whole Numbers Definition. The rational numbers whose values are completely positive. The same number is the whole number.

Quiz

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

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

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