The **whole numbers** room the component of the number system in i beg your pardon it includes all the hopeful integers indigenous 0 come infinity. This numbers exist in the number line. Hence, they are all actual numbers. We have the right to say, all the totality numbers are real numbers, however not all the genuine numbers are totality numbers. Thus, us can define whole numbers together the collection of organic numbers and also 0. Integers room the collection of whole numbers and an adverse of natural numbers. Hence, integers incorporate both positive and an unfavorable numbers consisting of 0. Real numbers space the set of every these varieties of numbers, i.e., organic numbers, whole numbers, integers and also fractions.

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The complete collection of natural numbers along with ‘0’ are dubbed whole numbers. The instances are: 0, 11, 25, 36, 999, 1200, etc.

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Table of contents:DefinitionProperties |

## Whole number Definition

The **whole numbers** room the numbers there is no fractions and it is a repertoire of hopeful integers and also zero. The is stood for by the price “W” and the set of numbers room 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………. Zero together a whole represents nothing or a null value.

Whole Numbers: W = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10……Natural Numbers: N = 1, 2, 3, 4, 5, 6, 7, 8, 9,…Integers: Z = ….-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,…Counting Numbers: 1, 2, 3, 4, 5, 6, 7,…. |

These numbers are hopeful integers including zero and do not incorporate fractional or decimal components (3/4, 2.2 and 5.3 space not totality numbers). Addition, Subtraction, Multiplication and department operations are possible on whole numbers.

**Symbol**

**The symbol to represent whole numbers is the alphabet ‘W’ in capital letters.**

**W = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,…**

**Thus, the whole number list contains 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ….**

**Facts:**

All the herbal numbers are whole numbersAll counting numbers are entirety numbersAll optimistic integers consisting of zero are totality numbersAll totality numbers are actual numbers |

If you still have doubt, What is a whole number in maths? A an ext comprehensive understanding of the totality numbers deserve to be obtained from the adhering to chart:

## Whole numbers Properties

The properties of whole numbers are based upon arithmetic work such together addition, subtraction, department and multiplication. Two whole numbers if included or multiplied will give a totality number itself. Subtraction of two totality numbers may not an outcome in entirety numbers, i.e. It have the right to be an essence too. Also, department of two totality numbers results in obtaining a fraction in some cases. Now, let us see some much more properties of whole numbers and also their proofs with the help of examples here.

**Closure Property**

**They deserve to be closed under addition and multiplication, i.e., if x and y room two whole numbers then x. Y or x + y is also a entirety number.**

**Example:**

5 and 8 are totality numbers.

5 + 8 = 13; a totality number

5 × 8 = 40; a entirety number

Therefore, the entirety numbers room closed under addition and multiplication.

**Commutative residential property of enhancement and Multiplication**

**The sum and product of two entirety numbers will certainly be the same whatever the order lock are added or multiplied in, i.e., if x and y are two totality numbers, then x + y = y + x and also x . Y = y . X**

**Example:**

Consider two whole numbers 3 and also 7.

3 + 7 = 10

7 + 3 = 10

Thus, 3 + 7 = 7 + 3 .

Also,

3 × 7 = 21

7 × 3 = 21

Thus, 3 × 7 = 7 × 3

Therefore, the totality numbers room commutative under addition and multiplication.

**Additive identity**

**When a whole number is added to 0, that value remains unchanged, i.e., if x is a totality number climate x + 0 = 0 + x = x**

**Example:**

Consider two entirety numbers 0 and also 11.

0 + 11 = 0

11 + 0 = 11

Here, 0 + 11 = 11 + 0 = 11

Therefore, 0 is called the additive identity of entirety numbers.

**Multiplicative identity**

**When a whole number is multiplied by 1, that is value stays unchanged, i.e., if x is a whole number then x.1 = x = 1.x**

**Example:**

Consider two totality numbers 1 and 15.

1 × 15 = 15

15 × 1 = 15

Here, 1 × 15 = 15 = 15 × 1

Therefore, 1 is the multiplicative identity of entirety numbers.

**Associative Property**

**When totality numbers room being added or multiplied as a set, they can be grouped in any order, and also the result will be the same, i.e. If x, y and also z are entirety numbers climate x + (y + z) = (x + y) + z and x. (y.z)=(x.y).z**

**Example:**

Consider three entirety numbers 2, 3, and also 4.

2 + (3 + 4) = 2 + 7 = 9

(2 + 3) + 4 = 5 + 4 = 9

Thus, 2 + (3 + 4) = (2 + 3) + 4

2 × (3 × 4) = 2 × 12 = 24

(2 × 3) × 4 = 6 × 4 = 24

Here, 2 × (3 × 4) = (2 × 3) × 4

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

**Distributive Property**

**If x, y and z are three whole numbers, the distributive home of multiplication over addition is x. (y + z) = (x.y) + (x.z), similarly, the distributive residential property of multiplication end subtraction is x. (y – z) = (x.y) – (x.z)**

**Example: **

Let us take into consideration three totality numbers 9, 11 and also 6.

9 × (11 + 6) = 9 × 17 = 153

(9 × 11) + (9 × 6) = 99 + 54 = 153

Here, 9 × (11 + 6) = (9 × 11) + (9 × 6)

Also,

9 × (11 – 6) = 9 × 5 = 45

(9 × 11) – (9 × 6) = 99 – 54 = 45

So, 9 × (11 – 6) = (9 × 11) – (9 × 6)

Hence, proved the distributive building of whole numbers.

### Multiplication by zero

When a entirety number is multiplied to 0, the an outcome is constantly 0, i.e., x.0 = 0.x = 0

**Example:**

0 × 12 = 0

12 × 0 = 0

Here, 0 × 12 = 12 × 0 = 0

Thus, any whole number multiply by 0, the an outcome is constantly 0.

### Division by zero

Division of a whole number by o is no defined, i.e., if x is a entirety number then x/0 is no defined.

**Also, check:** entirety number calculator

## Difference in between Whole Numbers and also Natural Numbers

**Difference in between Whole numbers & herbal Numbers**

Whole Numbers | Natural Numbers |

Whole Numbers: 0, 1, 2, 3, 4, 5, 6,….. | Natural Numbers: 1, 2, 3, 4, 5, 6,…… |

Counting starts native 0 | Counting starts indigenous 1 |

All totality numbers room not natural numbers | All organic numbers are entirety numbers |

Below number will assist us to understand the difference between the entirety number and natural number :

### Can entirety Numbers be negative?

The entirety number can’t be negative!

As per definition: 0, 1, 2, 3, 4, 5, 6, 7,……till confident infinity are entirety numbers. Over there is no place for an unfavorable numbers.

### Is 0 a whole number?

Whole numbers space the collection of every the natural numbers consisting of zero. For this reason yes, 0 (zero) is not just a entirety number however the an initial whole number.

## Solved Examples

**Example 1: **Are 100, 227, 198, 4321 entirety numbers?

**Solution: **Yes. 100, 227, 198, 4321 space all whole numbers.

**Example 2**: Solve 10 × (5 + 10) making use of the distributive property.

**Solution: ** Distributive property of multiplication end the addition of totality numbers is:

x × (y + z) = (x × y) + (x × z)

10 × (5 + 10) = (10 × 5) + (10 × 10)

= 50 + 100

= 150

Therefore, 10 × (5 + 10) = 150

However, we can present the several instances of entirety numbers making use of the entirety numbers properties.

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