Hello Students!
Before learning any topic in mathematics we should start with it’s basic facts to make our understanding more clear. In this chapter we will learn the following facts:
Learning Points:
- Definition of Number
- Types of Numbers with Definition and examples.
- Properties of Numbers.
- Operations of Numbers.
Definition:
A number is a mathematical value that is used for counting or measuring any object by using various mathematical operations like addition, subtraction, multiplication and division. In number system, numerical digits and some mathematical symbols are used for representing number.
Types of Numbers:
The various types of numbers in mathematics are as below:
- Whole Numbers
- Natural Numbers
- Integers
- Rational Numbers
- Irrational Numbers
- Decimal Numbers
- Real Numbers
Properties of Numbers:
The following are the key properties of number systems which are essential for performing mathematical operations and solving equations.
- Closure Property
- Commutative Property
- Associative Property
- Distributive Property
- Identity Property
- Inverse Property
Now let us define each of the above numbers with their properties using mathematical operations like addition, subtraction, multiplication and division.
Properties of Whole numbers:
- Whole numbers can be used in arithmetic operations like addition, subtraction, multiplication, and division.
- Whole numbers do not include negative numbers, decimals, or fractions.
Properties Under Arithmetical Operations
- Closure Properties
Under Addition
The sum of any two whole numbers is also a whole number. Let ‘a’ and ‘b’ be any two whole number, then a+b is also a whole number. This is called closure propertie of Whole number under addition and we can say that whole number is closed under addition.
For example: 0 and 4 are two whole numbers, hence 0+4=4 is also a whole number. Similarly 3 and 8 are two whole numbers, hence 3+8=11 is also a whole number.
Under Subtraction
For any two whole numbers ‘a’ and ‘b’ the value of a-b is a whole number only if a>b, unless the value of a-b is not a whole number. Hence whole number is closed under subtraction when a>b and not closed under subtraction when a<b.
For example: Let a=4 and b=3 are two whole numbers(where a>b), hence 4-3=1 is a whole number, but if a=3 and b=4, then 3-4=-1 is not a whole number since a<b.
Under Multiplication
Multiplication of any two whole numbers is also a whole number. Let a and b be any two whole numbers then the value of a×b is also a whole number. Hence whole number is closed under multiplication.
For example: 0 and 4 are two whole numbers, hence 0×4=0 is also a whole number. 3 and 8 are two whole numbers, hence 3×8=24 is also a whole number.
Under Division
For any two whole numbers ‘a’ and ‘b’ the value of a÷b in a/b form or in decimal number form is not a whole numbers. Hence whole number is not closed under division.
For example: 2 and 5 are two whole numbers, hence 2÷5=2/5 is not a whole number. Similarly 3 and 8 are two whole numbers, but 3÷8= 3/8 is not a whole number.
I hope the above explanation about closure property of the whole number may help the students to make their understanding clear.