The list of whole numbers 0 to 100 consists of all real numbers and zero. How come I didn’t just say natural numbers? This is so since natural numbers are a grouping of numbers that do not include zero and range from 1 to infinity. Whole numbers are the same as real numbers as they do not include any negative numbers or decimals in them. Whole numbers can also be used to describe counting numbers. We will be learning a lot more about the whole numbers today.

What is a Whole Number?

The set of counting numbers is referred to as natural numbers 1 to 1000, whereas numbers including 0 form the set of whole numbers. Zero carries a null value and is an undefined identity.

To keep it simple and more understandable, whole numbers are a set of numbers without fractions, decimals, and negative integers. Many kids find it difficult to identify the difference between whole numbers and natural numbers in their math classes.

Definition of Whole Number

Whole numbers are those in a set that don’t include any fractions, negative integers, or decimals. We can also define whole numbers as natural numbers and 0. It is represented by the alphabet “W”. In mathematics, the set is shown as {0, 1, 2, 3,…}.

Symbol of Whole Number

Whole numbers are denoted by capital ‘W’.

W = { 0, 1, 2, 3,….}

Difference Between Natural and Whole Numbers

Natural and whole numbers can be distinguished considerably by the number zero. Whole numbers begin with zero, whereas natural numbers do not. But natural numbers do not start with zero or contain zero in their number line.

Whole Numbers and Their Facts

Learning any concept with the help of a few facts makes math classes more fun. To make your online math classes more fun, here are a few facts about whole numbers:

Every natural number is a whole number

Whole numbers are used as counting numbers

Whole numbers consist of positive integers

Whole numbers start with zero

Properties of Whole Numbers

The essential functions such as Addition, subtraction, multiplication, and division in mathematics are also the properties that represent whole numbers.They are as follows:

Closure Property

Associative Property

Commutative Property

Distributive Property

Closure Property

The closure Property can only be used with addition and multiplication. Any two whole numbers add up to another whole number when they are multiplied or added together.

For example:

Closure property of addition: a+b=c ⇒ 6+5=11, 15+3=18(whole number).

Closure property of multiplication: axb = c ⇒ 3×5=15, 8×8=64(whole number).

Associative Property

Unlike the closure feature, the associative property only applies to the addition and multiplication of whole numbers. Even if the sequence varies, any three whole numbers added together or multiplied together provide a whole number.

For example:

Associative Property of addition: a+(b+c)=(a +b)+c ⇒ 2+(5+2)=9 and (2+5)+2=9.

Associative property of multiplication: ax(bxc)=(axb)xc ⇒ 3x(1×5)=3×5=15 and (3×1)x5=3×5=15.

Commutative Property

According to this characteristic, a whole number’s multiplication is dispersed throughout the sum or difference of the whole numbers.

Distributive property of addition, ax(b+c)=axb+axc.

Distributive property of subtraction, ax(b-c)=axb-axc

Distributive Property

Commutative property can be applied only to the sum and product of whole numbers. Even if the order of two whole numbers changes, their total or product will stay the same.

For example:

Sum of Commutative property: a+b=b+a ⇒ 8+9=17 and 9+8=17.

Product of Commutative property: axb=bxa ⇒ 3×4=12 and 4×3=12.

Important Points About Properties

When a number is added with 0, it stays the same. For example, 0+5=5,18+0=18.

When a number is multiplied by 0, the result will be 0. For example, 0x3=0, 47×0=47.

First and the Smallest Whole Number

The whole number starts from 0. So, 0 is the first and smallest whole number. The number between positive and negative integers on a number line is always zero. Zero is the only number that has a null value and is also a number that is neither negative nor positive. Therefore, zero is the first and smallest whole number.

No, the whole number can not be a negative integer.The whole number always starts from 0 to infinity. As we know, natural numbers are whole numbers, but not all whole numbers are natural numbers.

Whole numbers contain zero, whereas natural numbers do not, making this the primary and only distinction between the two types of numbers.

Conclusion

The set of counting numbers is referred to as natural numbers 1 to 1000, whereas natural numbers plus zero (0) form the set of whole numbers. Most of the kids get confused between natural and whole numbers. That’s why kids need special attention in their math classes while learning. {igebra.ai} is a global ed-tech company that provides math courses for kids, making kids fall in love with math.