Class 8 Maths-NCERT Solution-Rational Numbers

Rational Numbers

A rational number is a number that can be written in the form of P/Q where P and Q are integers and Q is not equal to 0.

Example:-5/7, (-2/3)

Properties of Rational numbers

We will first discuss the properties of rational numbers.

Closure Property

We call a set of numbers closed under operation if performance of that operation on members of the set of numbers always creates a member of the same set only; in this case we also say that the set is closed under the operation.

Under addition

Rational numbers are closed under addition.For any two rational numbers a and b,a+b is also a rational number.

Under subtraction

Rational numbers are closed under addition.For any two rational numbersaand b, a-b is also a rational number.

Under Multiplication

Rational statistics are closed under multiplication.For any two rational numbers a and b, a*b is also a rational number.

Under Division

Rational numbers are not closed under multiplication.For any rational number a, a/0 is not defined.

Commutative Property

As per commutative property, the interchanging order of numbers will not change the result.

Under addition

Two rational numbers can be added in any order.Addition is commutative for rational numbers.For any two rational numbers a and b, a+b=b+a

Under subtraction

Subtraction is not commutative for rational numbers.

Under Multiplication

Multiplication is commutative for rational numbers. For any two rational numbers a and b, a*b=b*a

Under Division

Division is not commutative for rational numbers

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