Exercise Of Whole Numbers

What are whole numbers and their examples?

Natural numbers, including zero, constitute a series of numbers that is often referred to as whole numbers. Zero seems to be an ambiguous digit that denotes a null series or no results. Whole numbers can be described in simple terms as a series or a set of digits that contain no type of fractions, any form of decimals, or even any form of negative integers. The whole numbers only include a series of positive integers or positive natural numbers, including zero, which is present at the starting point. Alternatively, whole numbers can always be defined as a collection of digits that don’t contain any non-negative integers. The inclusion of zero within the natural numbers to make it a series of whole number sets seems to be the major difference between natural and whole numbers.

Operation of Whole numbers with examples:

The whole numbers can always be added, subtracted, multiplied, and divided. The following are the ways of showing representing of these activities:

Addition: For example, when two whole numbers such as 20 and 40 are added to each other using the plus sign, the result comes out as a whole number, i.e., 20+40 = 60

Subtraction: For example, when two given whole numbers such as 60 and 40 are subtracted from each other using the minus sign, the result comes out as a whole number, i.e., 60-40 = 20.

Note, Sometimes the subtraction may result in negative integers such as 20 – 40 = -40. As -40 is not a positive integer, it cannot be categorised as a whole number. 

Multiplication: For example, when two whole numbers such as 60 and 40 are multiplied with each other using the cross sign, the result comes out as a whole number, i.e., 60×40 = 240.

Division: For example, when two given numbers such as 60 and 3 are divided from each other using the divide sign, the result comes out as a whole number, i.e., 60/3 = 20

Note, Sometimes the subtraction may result in negative integers such as 60/40 = 3/4. As 3/4 is not a positive integer and is a fraction, it cannot be categorised as a whole number.

Properties and examples of natural numbers:

Closure property: The closure property regarding the whole number states that if two whole numbers are added or multiplied, the restaurant number will always be a positive whole number; this property isn’t true in the case of subtraction as well as division as both of those operants may result in a negative integer or a negative natural number and that doesn’t satisfy the definition of a whole number.

For Example : In addition,

400+500 = 900

36 + 14 = 50 and so on, 

In multiplication,

8×8 = 64

25x 4 = 100 and so on. 

Note,The addition and multiplication will always produce positive natural numbers.

Examples of Subtraction and division: 

Sub: 5-3 = 2. Here the result is a whole number but,

In the given problem 4-8= -8, the result is a negative integer and doesn’t satisfy the whole number properties.

Division –  80/60 = 4/3, as the result is a fraction the number cannot be recognised as a whole number.

Associative property: The associative property defines itself as, when three given whole numbers are altered in any form or order, their product as well as sum will always be the same and will always be a positive natural number. The associative property, when applied to subtraction and division, doesn’t result in a positive integer every time, but in the case of addition and multiplication, it seems to always result in a positive integer, hence satisfying the properties of a whole number.

For Example : (8+6)+4 = 18, 

6+(8+4) = 18.

As you can see, the result is always the same regardless of the order and is always a positive integer.

(6×2)x5 =  = 60

 2x(5×6) = 60

As you can see, the result is always the same regardless of the order and is always a positive integer when using multiplication.

Commutative property: The commutative property seems to be similar in some ways when compared to the associative property. It says that when two numbers are reversed or altered, their results remain the same. This property applies to addition and multiplication when whole numbers are considered as a value, but subtraction and division may sometimes result in negative integers.

For example, 8+4 = 12 and when it is reversed as 4+8, the result remains the same as well as a positive integer hence satisfying the whole number property.

In the same way,

Multiplication: 4×6 = 24

6×4 = 24

Division: 12/6 = 2

6/12 = ½ which is a fraction, hence it doesn’t satisfy the properties of a whole number.It is the same in case of subtraction.

Distributive property: Distributive property of multiplication over addition:

Example: 

Addition : a × (b + c) = ab + ac,  8x(6+4) = 80 &

 8×6 – 8 x 4 = 48 + 32 = 80

Distributive property of multiplication over subtraction:

Subtraction : a × (b – c) = ab – ac 8x(6-4) = 16 &

 8×6 – 8 x 4 = 48 – 32 = 16

Conclusion:

This article talks briefly about the whole numbers and also present detailed examples regarding them. Whole numbers seem to be a series of numbers that contain zero as their starting point unlike natural numbers that start with one. They have similar properties when compared to natural numbers.