Is 6/3 A Whole Number

The whole numbers are the part of the number organization which includes all the positive integers from 0 to infinity. These numbers be in the number line. Hence, they are all existent numbers . Nosotros can say, all the whole numbers are real numbers, but not all the real numbers are whole numbers. Thus, we can define whole numbers as the set of natural numbers and 0. Integers are the set of whole numbers and negative of natural numbers. Hence, integers include both positive and negative numbers including 0. Real numbers are the ready of all these types of numbers, i.due east., natural numbers, whole numbers, integers and fractions.

The consummate set of natural numbers along with '0' are called whole numbers. The examples are: 0, 11, 25, 36, 999, 1200, etc.

Acquire more well-nigh numbers here.

Table of contents:

Definition
- Symbol
Backdrop
- Closure
- Commutative
- Additive
- Multiplicative
- Associative
- Distributive
Whole Numbers and Natural numbers
Solved Examples
Do Problems
Video Lesson
FAQs

Whole Numbers Definition

The whole numbers are the numbers without fractions and information technology is a collection of positive integers and zero. Information technology is represented past the symbol "W" and the set of numbers are {0, 1, ii, 3, four, five, 6, vii, eight, nine,……………}. Zero as a whole represents nothing or a aught value.

Whole Numbers: W = {0, i, 2, 3, 4, 5, half dozen, 7, 8, 9, 10……}
Natural Numbers: North = {1, 2, 3, iv, five, 6, seven, viii, 9,…}
Integers: Z = {….-ix, -8, -7, -half dozen, -v, -4, -three, -two, -1, 0, 1, two, 3, 4, 5, 6, 7, viii, 9,…}
Counting Numbers: {1, 2, three, 4, 5, 6, 7,….}

These numbers are positive integers including zero and practise non include partial or decimal parts (three/4, 2.2 and 5.iii are not whole numbers). Also, arithmetic operations such equally addition, subtraction, multiplication and division are possible on whole numbers.

Symbol

The symbol to represent whole numbers is the alphabet 'W' in upper-case letter letters.

West = {0, one, two, three, four, 5, 6, 7, eight, 9, 10,…}

Thus, the whole numbers listing includes 0, 1, ii, iii, four, five, 6, 7, 8, ix, ten, eleven, 12, ….

Facts:

All the natural numbers are whole numbers
All counting numbers are whole numbers
All positive integers including zero are whole numbers
All whole numbers are real numbers

If you lot yet accept doubt, What is a whole number in maths? A more comprehensive understanding of the whole numbers can exist obtained from the following chart:

Real number system

Whole Numbers and Natural Numbers
Natural Numbers
Difference Between Natural and Whole numbers
Important Questions For Class half-dozen Maths

Whole Numbers Properties

The properties of whole numbers are based on arithmetics operations such equally addition, subtraction, sectionalisation and multiplication. Ii whole numbers if added or multiplied will give a whole number itself. Subtraction of two whole numbers may non result in whole numbers, i.e. it can be an integer too. Also, the division of ii whole numbers results in getting a fraction in some cases. At present, let u.s.a. run across some more than backdrop of whole numbers and their proofs with the aid of examples hither.

Closure Property

They can be airtight nether improver and multiplication, i.e., if x and y are two whole numbers and then x. y or ten + y is too a whole number.

Instance:

5 and 8 are whole numbers.

five + 8 = 13; a whole number

5 × 8 = forty; a whole number

Therefore, the whole numbers are airtight under addition and multiplication.

Commutative Property of Addition and Multiplication

The sum and product of two whole numbers volition be the aforementioned whatever the guild they are added or multiplied in, i.e., if x and y are two whole numbers, then x + y = y + x and x . y = y . x

Example:

Consider two whole numbers 3 and 7.

3 + seven = 10

7 + 3 = ten

Thus, 3 + vii = 7 + 3 .

Besides,

iii × seven = 21

7 × 3 = 21

Thus, 3 × 7 = 7 × iii

Therefore, the whole numbers are commutative nether addition and multiplication.

Condiment identity

When a whole number is added to 0, its value remains unchanged, i.e., if x is a whole number and so x + 0 = 0 + ten = x

Example:

Consider two whole numbers 0 and 11.

0 + 11 = 11

11 + 0 = xi

Here, 0 + 11 = 11 + 0 = 11

Therefore, 0 is called the condiment identity of whole numbers.

Multiplicative identity

When a whole number is multiplied past 1, its value remains unchanged, i.e., if x is a whole number then x.1 = x = 1.x

Example:

Consider two whole numbers 1 and xv.

one × 15 = fifteen

15 × ane = 15

Hither, 1 × 15 = fifteen = 15 × 1

Therefore, one is the multiplicative identity of whole numbers.

Associative Property

When whole numbers are being added or multiplied every bit a set up, they can be grouped in whatever order, and the result will be the aforementioned, i.e. if 10, y and z are whole numbers then ten + (y + z) = (10 + y) + z and x. (y.z)=(x.y).z

Case:

Consider three whole numbers 2, 3, and 4.

two + (3 + 4) = 2 + vii = nine

(two + three) + 4 = five + 4 = 9

Thus, 2 + (3 + four) = (ii + three) + iv

2 × (3 × 4) = two × 12 = 24

(2 × 3) × 4 = 6 × 4 = 24

Here, ii × (3 × 4) = (2 × 3) × 4

Therefore, the whole numbers are associative under addition and multiplication.

Distributive Property

If x, y and z are iii whole numbers, the distributive belongings of multiplication over addition is x. (y + z) = (x.y) + (x.z), similarly, the distributive property of multiplication over subtraction is x. (y – z) = (x.y) – (ten.z)

Example:

Let us consider three whole numbers 9, 11 and 6.

ix × (11 + vi) = 9 × 17 = 153

(9 × 11) + (9 × 6) = 99 + 54 = 153

Hither, 9 × (11 + 6) = (ix × 11) + (9 × vi)

Likewise,

9 × (11 – six) = 9 × 5 = 45

(9 × eleven) – (9 × 6) = 99 – 54 = 45

And then, 9 × (11 – 6) = (ix × 11) – (9 × 6)

Hence, verified the distributive property of whole numbers.

Multiplication by zero

When a whole number is multiplied to 0, the consequence is always 0, i.e., x.0 = 0.ten = 0

Example:

0 × 12 = 0

12 × 0 = 0

Here, 0 × 12 = 12 × 0 = 0

Thus, for any whole number multiplied by 0, the result is always 0.

Sectionalization by naught

The division of a whole number by o is not divers, i.e., if 10 is a whole number then x/0 is non defined.

Too, check: Whole number computer

Divergence Between Whole Numbers and Natural Numbers

Deviation Betwixt Whole Numbers & Natural Numbers
Whole Numbers	Natural Numbers
Whole Numbers: {0, 1, 2, iii, 4, 5, 6,…..}	Natural Numbers: {i, 2, 3, 4, 5, 6,……}
Counting starts from 0	Counting starts from ane
All whole numbers are not natural numbers	All Natural numbers are whole numbers

The below effigy will assist us to understand the deviation between the whole number and natural numbers :

Whole numbers-Number line

Can Whole Numbers be negative?

The whole number can't exist negative!

As per definition: {0, one, two, 3, 4, v, 6, 7,……till positive infinity} are whole numbers. In that location is no place for negative numbers.

Is 0 a whole number?

Whole numbers are the set of all the natural numbers including zero. So yes, 0 (zero) is not just a whole number simply the first whole number.

Solved Examples

Example i:Are 100, 227, 198, 4321 whole numbers?

Solution:Yep. 100, 227, 198, and 4321 are all whole numbers.

Example 2: Solve 10 × (five + 10) using the distributive property.

Solution: Distributive property of multiplication over the addition of whole numbers is:

x × (y + z) = (x × y) + (x × z)

10 × (five + 10) = (10 × 5) + (x × x)

= 50 + 100

= 150

Therefore, 10 × (5 + 10) = 150

Nonetheless, nosotros can show several examples of whole numbers using the properties of the whole numbers.

Practise Bug

Write whole numbers between 12 and 25.
What is the additive inverse of the whole number 98?
How many whole numbers are there between -1 and 14?

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Video lesson

Frequently Asked Questions on Whole Numbers

What are whole numbers?

The whole numbers are divers as positive integers including zero. The whole number does non contain any decimal or fractional part. It means that it represents the entire affair without pieces. The set of whole numbers is mathematically represented every bit:
W = (0, 1, 2, 3, 4, 5,……}

Can whole numbers be negative?

No, the whole numbers cannot be negative. The whole numbers start from 0, 1, 2, 3, … so on. All the natural numbers are considered as whole numbers, but all the whole numbers are not natural numbers. Thus, the negative numbers are non considered as whole numbers.

What are the properties of whole numbers?

The properties of whole numbers are:
Whole numbers are closed nether improver and multiplication
The addition and multiplication of whole numbers is commutative
The addition and multiplication of whole numbers is associative
It obeys the distributive property of multiplication over addition
The additive identity of whole numbers is 0
The multiplicative identity of whole numbers is 1

Is 10 a whole number?

x is a whole also as a natural number. Information technology is written as Ten in words. Although -x as well represents a whole and not a fraction.

Which numbers are not whole numbers?

The numbers which do not exist between 0 and infinity are not whole numbers. Negative integers, fractions or rational numbers are not whole numbers. Examples are -1, -5, ½, nine/4, pi, etc. are non whole numbers.

Are all whole numbers real numbers?

Real numbers are those numbers that include rational numbers, integers, whole numbers and natural numbers. All whole numbers are real numbers but non all real numbers are whole.

Are all natural numbers, whole numbers?

Natural numbers are those which start from 1 and stop at infinity, whereas whole numbers start from 0 and terminate at infinity. All the natural numbers are whole numbers merely not all whole numbers are natural.

Are natural numbers and counting numbers the same?

Natural numbers are the numbers starting from 1 and extend up to infinity. Counting numbers are used to count the objects or people or anything which is countable. Hence, we always start counting from one.