Learn Class 8 Math - Rational Numbers

Many mathematical processes, including addition, subtraction, and multiplication, are inherently closed when they concern rational numbers.

Introduction to Rational Numbers

Rational numbers are fractions of two integers, denoted by p/q, where q must not be zero. A set of rational numbers is called Q.

For example: A rational number, 5/7, is an integer where -5 and 7 are integers.

Since 2 can be written as 2/1 where both 2 and 1 are integers, even 2 is a rational number.

Rational Numbers: Their properties

• Rational numbers are always fractions, but fractions are not always rational numbers.
• There are no positive or negative rational numbers equal to 0.
• Rational numbers always exceed their left-hand side counterparts on a number line.
• Any rational number multiplied by its reciprocal will result in 1.

Rational numbers possess the following properties:

• Closure Property - In the same type, obtaining another number when you operate (multiplication, division, subtraction, etc.) on any two numbers is called the Closure Property.
• Commutative Property - By definition, the Commutativity Property states that the order of numbers does not matter. If you reverse the order of two numbers (by addition, multiplication, subtraction, etc.), the result is the same as if they were kept together.
• Associative Property - Using the Associative Property, we can add parenthesis anywhere, and we will get the same answer regardless of the order in which the numbers are grouped (i.e., calculated first).