Natural Numbers in Real Life Situations

In the field of mathematics, counting and ordering items are done using natural numbers. This set of numbers has been used in everyday activities. Natural numbers are the set of numbers that start from the numeral 1 and can extend up to infinity. They are sub-categorised under real numbers. Zero is not a part of this set of numbers. Hence, number one (1) is the smallest known natural number. The natural number set does not include – negative numbers, fractional numbers, and decimal numbers. The properties of natural numbers like divisibility and prime number distribution are elucidated in the number theory. The alphabet N is used as a symbol to address natural numbers. Hence, the set of numbers is represented as N = {1,2,3,4,……….}. In the further sections, we will see the properties of natural numbers and the real-life applications of natural numbers. 

Major algebraic properties of natural numbers 

Four algebraic operations are performed by natural numbers are – multiplication, addition, division, and subtraction. These 4 operations lead to the four prime properties that make natural numbers unique. The properties are – closure property, distributive property, associative property, and commutative property. 

1. Closure property 

This property of natural numbers is true over the operations of addition and multiplication. It says that when we sum up or multiply any two natural numbers, it will always result in a natural number.

• Closure property of natural numbers for addition 

The property is expressed as ( C + D = E) 

Where C, D, and E are all natural numbers 

Example – 3 + 4 = 7 

Here, 3, 4, and 7 are natural numbers. So this property is true.

• Closure property of natural numbers for multiplication 

This property is expressed as ( C ✕ D = E) 

Where C, D, and E are all natural numbers 

Example – 5 ✕ 6 = 30 

Here, 5,6, and 30 are natural numbers. Hence, this property is true for multiplication.

Now let us see why the closure property is not for the division and subtraction operations. 

• An example for subtraction – 2 – 3 = -1 ( it is a negative number, hence it is not a natural number) 

• An example for division = 10/4 = 2.5 ( it is a decimal number, hence it is not a natural number) 

2. Distributive property 

This property of natural numbers states that when an expression is of the form C ✕ ( D + E) or C ✕ (D – E), the C operand can be distributed over the other two operands D and E 

• The distributive property of multiplication is always true when it is distributed over the addition operation C ✕ ( D + E) = C ✕ D + C ✕ E 

Example – 4 ✕ ( 5 +3 ) = 4 ✕ 5 + 4 ✕ 3 = 32 

• The distributive property of multiplication is always true when it is distributed over the subtraction operation C ✕ ( D – E) = C ✕ D – C ✕ E 

Example – 1 ✕ ( 4 – 3 ) = 1 ✕ 4 – 1 ✕ 3 = 1 

3. Associative property 

This property of natural numbers says that when the grouping of three natural numbers is changed, the answer will remain the same when the operation is multiplication or addition. This property is not true for the operations of subtraction and division.

• The Associative property applied over addition 

It is expressed as C + ( D + E) = ( C+D) + E 

Example – 3 + ( 4 + 5) = ( 3 + 4) + 5 = 12 

3, 4, 5, and 12 are natural numbers. Hence, this property is true for addition.

• The Associative property applied over multiplication 

It is expressed as C ✕ ( D ✕ E) = ( C ✕ D) ✕ E 

Example – 1 ✕ ( 2 ✕ 3) = ( 1 ✕ 2) ✕ 3 = 6

1, 2, 3, and 6 are natural numbers. Hence, this property is true for addition.

4. The Commutative property 

This property of natural numbers says that when the places of any two natural numbers are interchanged for the addition and multiplication operation, then the result will remain unchanged. 

• The Commutative property applied over addition

It is expressed as C + D = D + C

Example – 3 + 4 = 4 + 3 = 7 

Here, 3,4, and 7 are natural numbers. Hence, this property is true for addition. 

• The Commutative property applied over multiplication 

It is expressed as C ✕ D = D ✕ C

Example – 5 ✕ 8 = 8 ✕ 5 = 40 

Here, 8,5, and 40 are natural numbers. Hence, this property is true for multiplication.

What are the real-life applications of natural numbers?

In this section, we will see how natural numbers can be used in everyday activities. The two predominant daily applications of natural numbers are ordering and counting.

• Counting – in this application, we have to count the specific amount of objects by assigning the first object to the natural number 1. The next object will be assigned the number 2 and so on until all the objects are counted. Counting is also known as enumeration

• Ordering – Ordering is also known as ranking the objects. For orders, we have to first select the object with an extreme value (example – tallest, smallest, etc.) and we will assign this object with the natural number 1. The next object with the second-highest or extreme value will be assigned with the number 2 and so on the ranking will continue

Conclusion 

Here, we have discussed the algebraic properties of natural numbers and the applications of natural numbers. Natural numbers are the set of numbers that start from the numeral 1 and can extend up to infinity. The alphabet N is used as a symbol to address natural numbers. The natural number set does not include – negative numbers, fractional numbers, and decimal numbers. The properties of natural numbers are – closure property, distributive property, associative property, and commutative property. These properties make the natural number set unique. The two predominant daily applications of natural numbers are ordering and counting.