Whole numbers space a collection of numbers including all confident integers and also 0. Whole numbers space a part of actual numbers that carry out not incorporate fractions, decimals, or negative numbers. Counting numbers are likewise considered overall numbers. In this lesson, we will learn whole numbers and also related concepts. In mathematics, the number system is composed of all species of numbers, including organic numbers and whole numbers, element numbers and composite numbers, integers, genuine numbers, and also imaginary numbers, etc., which space all supplied to perform miscellaneous calculations.

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We check out numbers everywhere about the world, because that counting objects, for representing or exchanging money, because that measuring the temperature, informing time, etc. There is practically nothing that doesn't indicate numbers, it is in it complement scores, cooking recipes, count on objects, etc.

1. | What are whole Numbers? |

2. | Whole numbers vs organic Numbers |

3. | Whole number on Number Line |

4. | Properties of whole Numbers |

5. | FAQs on totality Numbers |

## What are entirety Numbers?

Natural numbers refer to a set of optimistic integers and on the other hand, organic numbers in addition to zero(0) kind a set, referred to all at once numbers. However, zero is one undefined identity that to represent a null set or no an outcome at all.

In basic words, entirety numbers space a set of numbers there is no fractions, decimals, or even an adverse integers. The is a collection of hopeful integers and zero. The main difference in between natural and whole number is zero.

**Whole Number Definition:**

Whole Numbers room the set of natural numbers in addition to the number 0. The set of whole numbers in math is the set 0, 1,2,3,....This set of totality numbers is denoted by the symbol** W.**

W = 0,1,2,3,4…

Here room some facts around whole numbers, i m sorry will help you recognize them better:

All herbal numbers are totality numbers.All counting number are totality numbers.All optimistic integers consisting of zero are whole numbers.All whole numbers are genuine numbers.### Whole Number Symbol

The symbol provided to represent whole numbers is the alphabet ‘W’ in resources letters, W = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,…

### Smallest entirety Number

**Whole numbers begin from 0 **(from the an interpretation of whole numbers). Thus, 0 is the smallest entirety number. The principle of zero was very first defined by a Hindu astronomer and mathematician Brahmagupta in 628. In straightforward language, zero is a number the lies between the confident and an adverse numbers on a number line. Return zero dead no value, it is supplied as a placeholder. So, zero is neither a hopeful number no one a an unfavorable number.

## Whole number vs organic Numbers

From the above definitions, we can understand the every totality number various other than 0 is a natural number. Also, every herbal number is a totality number. So, the collection of herbal numbers is a part of the collection of totality numbers or a subset of entirety numbers.

### Difference between Whole numbers and also Natural numbers

Let us understand the difference between whole numbers and also natural numbers with the table offered below:

Whole NumberNatural NumberThe collection of totality numbers is, W=0,1,2,3,... | The collection of herbal numbers is, N= 1,2,3,... |

The smallest totality number is 0. | The smallest natural number is 1. |

Every organic number is a whole number. | Every whole number is a natural number, except 0. |

## Whole number on Number Line

The collection of natural numbers and also the set of entirety numbers deserve to be shown on the number heat as given below. All the hopeful integers or the integers top top the right-hand side of 0, stand for the natural numbers, whereas every the optimistic integers together with zero, altogether stand for the totality numbers. Both set of numbers have the right to be represented on the number line together follows:

## Properties of entirety Numbers

The straightforward operations on whole numbers: addition, subtraction, multiplication, and division, lead to four main properties of totality numbers the are provided below:

Closure PropertyAssociative PropertyCommutative PropertyDistributive Property**Closure Property**

The sum and also product the two entirety numbers is constantly a totality number. Because that example, 7 + 3 = 10 (whole number), 7 × 2 = 14 (whole number)

**Associative Property**

The sum or product of any three entirety numbers remains the same even if the group of number is changed. Because that example, once we add the complying with numbers we acquire the same sum: 10 + (7 + 12) = (10 + 7) + 12 = (10 + 12) + 7 = 29. Similarly, when we main point the following numbers we obtain the very same product no matter how the numbers are grouped: 3 × (2 × 4) = (3 × 2) × 4 = 24.

**Commutative Property**

The sum and also the product of two totality numbers remain the same even after interchanging the bespeak of the numbers. This home states that change in the order of addition does not adjust the value of the sum. Let 'a' and also 'b' it is in two whole numbers, follow to the commutative home a + b = b + a. For example, a = 10 and b = 19 ⇒ 10 + 19 = 29 = 19 + 10. It means that the entirety numbers room closed under addition. This property likewise holds true because that multiplication, however not because that subtraction or division. Because that example: 7 × 9 = 63 and 9 × 7 = 63.

**Additive identity**

When a entirety number is added to 0, its value stays unchanged, i.e., if x is a whole number climate x + 0 = 0 + x = x. For example, 3 + 0 = 3

**Multiplicative identity**

When a totality number is multiplied by 1, the value continues to be unchanged, i.e., if x is a totality number climate x.1 = x = 1.x. For example. 4 × 1 = 4

**Distributive Property**

This residential or commercial property states that the multiplication the a entirety number is dispersed over the amount of the totality numbers. It way that when two numbers, take it for instance a and b room multiplied v the exact same number c and are then added, then the sum of a and b can be multiply by c to gain the exact same answer. This situation can be represented as: a × (b + c) = (a × b) + (a × c). Let a = 10, b = 20 and also c = 7 ⇒ 10 × (20 + 7) = 270 and also (10 × 20) + (10 × 7) = 200 + 70 = 270. The same building is true for subtraction together well. Because that example, we have a × (b − c) = (a × b) − (a × c). Permit a = 10, b = 20 and c = 7 ⇒ 10 × (20 − 7) = 130 and also (10 × 20) − (10 × 7) = 200 − 70 = 130.

**Multiplication by zero**

When a totality number is multiplied to 0, the result is always 0, i.e., x.0 = 0.x = 0. Because that example, 4 × 0 = 0

**Division by zero**

Division that a entirety number through o is not defined, i.e., if x is a entirety number then x/0 is no defined.

For much more information about the nature of totality numbers, click here.

**Important Points**

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**Example 2: Is W close up door under subtraction and also division?**

**Solution:**

Whole numbers include only the positive integers and also zero. We understand that on individually one optimistic integer by another, we might not acquire their difference as a hopeful integer, similarly, on separating one optimistic number through another, we might not gain the quotient as a identified number for example in the situation of 13/0. Thus, for any two totality numbers, your difference and also quotient acquired may not be entirety numbers. Therefore, W is not closed under subtraction and division.

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**Example 3: because that the whole number worths of a, b, and c, that is, a = 3, b = 2, c = 1, prove a × (b + c) = (a × b) + (a × c)**

**Solution:**

Substituting the values of a, b, and c, we get: a × (b + c) = 3 × (2 + 1) = 3 × 3 = 9 and (a × b) + (a × c) = (3 × 2) + (3 × 1) = 6 + 3 = 9. Since, LHS = RHS, 9 = 9, thus, a × (b + c) = (a × b) + (a × c), for the given whole number values. This is recognized as the distributive property of multiplication of totality numbers.