The **whole numbers** are the part of the number system in which it consists of all the hopeful integers native 0 come infinity. These numbers exist in the number line. Hence, they room all real numbers. We can say, all the whole numbers are real numbers, but not every the actual numbers are entirety numbers. Thus, us can specify whole numbers together the set of natural numbers and 0. Integers are the collection of whole numbers and an adverse of herbal numbers. Hence, integers encompass both hopeful and an unfavorable numbers consisting of 0. Real numbers are the set of all these types of numbers, i.e., natural numbers, entirety numbers, integers and also fractions.

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

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Table the contents:DefinitionProperties |

## Whole number Definition

The **whole numbers** are the numbers there is no fractions and it is a collection of optimistic integers and zero. It is stood for by the symbol “W” and the set of numbers space 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………. Zero as a entirety 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 number are hopeful integers consisting of zero and also do not include fractional or decimal parts (3/4, 2.2 and 5.3 space not totality numbers). Addition, Subtraction, Multiplication and division operations are feasible on entirety numbers.

**Symbol**

**The symbol to represent entirety numbers is the alphabet ‘W’ in resources letters.**

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

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

**Facts:**

All the herbal numbers are totality numbersAll counting numbers are whole numbersAll confident integers including zero are entirety numbersAll totality numbers are actual numbers |

If girlfriend still have actually doubt, What is a entirety number in maths? A much more comprehensive understanding of the whole numbers have the right to be obtained from the complying with chart:

## Whole numbers Properties

The properties of whole numbers are based upon arithmetic to work such as addition, subtraction, department and multiplication. Two whole numbers if included or multiply will give a entirety number itself. Individually of two totality numbers may not an outcome in totality numbers, i.e. It deserve to be an creature too. Also, division of two totality numbers results in gaining a portion in some cases. Now, let united state see some much more properties of entirety numbers and their proofs with the assist of examples here.

**Closure Property**

**They can be close up door under enhancement and multiplication, i.e., if x and also y space two whole numbers climate x. Y or x + y is additionally a whole number.**

**Example:**

5 and also 8 are entirety numbers.

5 + 8 = 13; a entirety number

5 × 8 = 40; a totality number

Therefore, the whole numbers are closed under enhancement and multiplication.

**Commutative residential or commercial property of enhancement and Multiplication**

**The sum and product that two whole numbers will be the same everything the order lock are added or multiplied in, i.e., if x and also y space two entirety numbers, climate x + y = y + x and also x . Y = y . X**

**Example:**

Consider two whole numbers 3 and 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 whole numbers are commutative under addition and multiplication.

**Additive identity**

**When a entirety number is included to 0, that is value stays unchanged, i.e., if x is a entirety number then x + 0 = 0 + x = x**

**Example:**

Consider two entirety numbers 0 and 11.

0 + 11 = 0

11 + 0 = 11

Here, 0 + 11 = 11 + 0 = 11

Therefore, 0 is referred to as the additive identification of totality numbers.

**Multiplicative identity**

**When a entirety number is multiply by 1, that is value continues to be unchanged, i.e., if x is a whole number then x.1 = x = 1.x**

**Example:**

Consider two totality numbers 1 and also 15.

1 × 15 = 15

15 × 1 = 15

Here, 1 × 15 = 15 = 15 × 1

Therefore, 1 is the multiplicative identification of whole numbers.

**Associative Property**

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

**Example:**

Consider three totality numbers 2, 3, and 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 totality numbers are associative under enhancement and multiplication.

**Distributive Property**

**If x, y and also z room three totality numbers, the distributive property of multiplication over enhancement is x. (y + z) = (x.y) + (x.z), similarly, the distributive residential property of multiplication over subtraction is x. (y – z) = (x.y) – (x.z)**

**Example: **

Let us consider three entirety numbers 9, 11 and 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, verified the distributive residential or commercial property of totality numbers.

### Multiplication by zero

When a whole number is multiply 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 multiplied by 0, the an outcome is constantly 0.

### Division through zero

Division the a totality number by o is no defined, i.e., if x is a totality number then x/0 is not defined.

**Also, check:** whole number calculator

## Difference in between Whole Numbers and Natural Numbers

**Difference in between Whole number & 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 from 0 | Counting starts from 1 |

All entirety numbers space not herbal numbers | All herbal numbers are totality numbers |

Below figure will assist us to recognize the difference between the totality number and also natural number :

### Can whole Numbers it is in negative?

The totality number can’t be negative!

As every definition: 0, 1, 2, 3, 4, 5, 6, 7,……till optimistic infinity are whole numbers. There is no place for an adverse numbers.

### Is 0 a entirety number?

Whole numbers room the set of all the organic numbers including zero. Therefore yes, 0 (zero) is not just a totality number however the very first whole number.

## Solved Examples

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

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

**Example 2**: Solve 10 × (5 + 10) utilizing the distributive property.

**Solution: ** Distributive building of multiplication over 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, us can present the several examples of entirety numbers making use of the entirety numbers properties.

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