# Introduction of Rational Numbers

Before we start the introduction of rational numbers let us recall that for two given integers a and b, their sum a + b, product a × b and the difference a - b are always integers.

However, it may not always be possible for a given integer to exactly divide another given integer means the result of division of an integer by a non- zero integers may or may not be an integer. For example, when 9 is divided by 4, the result is not an integer since we know 9/4 is a fraction. Thus, there is need to extend the system of integers so that it may also be possible to divide any given integer by any other given integer different from zero (because division by zero is not possible).

Now, we shall introduce the system of rational numbers, comparison of rational numbers, representation of rational numbers on the number line, various operations on rational numbers and the properties of these operations on rational numbers.

Rational Numbers

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

Equivalent form of Rational Numbers

Rational Number in Different Forms

Properties of Rational Numbers

Lowest form of a Rational Number

Standard form of a Rational Number

Equality of Rational Numbers using Standard Form

Equality of Rational Numbers with Common Denominator

Equality of Rational Numbers using Cross Multiplication

Comparison of Rational Numbers

Rational Numbers in Ascending Order

Representation of Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Simplify Rational Expressions Involving the Sum or Difference

Multiplication of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

To Find Rational Numbers

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