Properties Of Natural Numbers

What are natural numbers and their properties?

Natural numbers seem to represent positive integers that range from one to infinity. These are all just figures that we frequently count throughout our daily lives. Fractions, decimals, negative values, including zero, are not considered as natural numbers. The letter ‘N’ is usually used for denoting a set of Natural Numbers. Every natural number is a whole number.

Natural numbers seem to be the figures that represent quantities that get utilised for numbering the value and order. In everyday speech, numerals that seem to get used for counting are referred to as cardinal numbers, and phrases that are used for sorting are referred to as ordinal numbers. Natural numbers can often exist as a handy collection of codes, which linguistics researchers refer to as nominal numbers, omitting most or even all of the mathematical attributes of being an integer.

Operation of natural numbers:

The natural numbers can be added, subtracted, multiplied and divided with each other. The symbol that represents all these activities is are called as follows:

• Addition: It is denoted by a plus sign “+” and functions as a summing tool. For example : 2+2 = 4
• Subtraction: It is denoted by a minus sign “-” and functions as a deduction tool. For example : 3+2 = 1
• Multiplication: It is denoted by a plus sign “x” and functions as a product tool. For example : 2×3 = 6
• Division: It is denoted by a plus sign “*/*” and functions as a dividing tool. For example : 10+2 = 5

Properties of natural numbers:

Using the various operators like addition, subtraction, multiplication and division, various formulas and methods have been derived for efficient calculations. These properties are called as follows:

• Closure property
• Associative property
• Commutative property
• Distributive property

Closure property: When two or multiple more natural numbers are added as well as multiplied, the result seems to be always a natural number. Natural numbers also have a property that says that they do not respect the closure principle when it comes to subtraction as well as division. As a result, subtracting or dividing a given number of natural numbers may not result in a natural number.

Example: 4+4 = 8, 6×6 = 36 and so on. The addition and multiplication will always produce positive natural numbers.

Associative property: When it comes to natural numbers and their addition as well as multiplication, the associative property results in positive natural numbers. The property says that, when given, three numbers are altered in any form or order and the product, as well as sum, will always be a positive natural number. The associative property, when applied to subtraction and division, does not doesn’t result in a positive natural number in every instance.

Example : (4+6)+2 = 12, (6×7)x3 = 126 and 6+(4+2) = 12, 7x(6×3) = 126 and so on. The addition and multiplication will always produce positive natural numbers.

Commutative property: The addition, as well as multiplication regarding natural numbers, always seems to demonstrate the commutative property being true and all results being positive natural numbers. Whereas in the case of Subtraction as well as the division of natural numbers, they do not seem to satisfy the commutative property. The property says that when two numbers are replaced and reversed, their sum and product will always result in positive natural numbers.

Example: 4+6 = 10, 6×7 = 42 and 6+4 = 10,7×6 = 42 and so on. The addition and multiplication will always produce positive natural numbers.

For subtraction and division = 4-6 = -2, 6/2 = 3 and 6-4 = 2, 2/6 = ⅓, the following example shows that the commutative property doesn’t produce positive natural numbers. 

Distributive property: The outcome of multiplication of the sum of two or more added numbers by a number is the same as multiplying each with each other separately and then adding the resultant values together.

Multiplication of natural numbers always seems to be distributive over the addition. The distributive property also has a property where multiplication is also distributive over subtraction.

Example: 

Addition – a × (b + c) = ab + ac, 2x(3+2) = 2×3 + 2×2 = 10

Subtraction – a × (b – c) = ab – ac 2x(3-2) = 2×3 – 2×2 = 2

Conclusion:

This article talks in brief about natural numbers and talks about how natural numbers work in different scenarios. The article gives us unique examples regarding the natural numbers and their properties and mentions efficient ways for making use, i.e. calculating the natural numbers.