Downloading Link is given at Last. What are rational numbers? A number that can be written aswhere p and q are integers and q 0, is known as Rational Number. Example:12. Read : Integers. If the btjus of numerator and denominator are either nunbers positive or both negative, the rational number is known as Positive Byjuus Number.

Example:. If the signs of numerator and denominator are opposite to each other, the rational number is known as Negative Rational Number. How many rrational of rational numbers? There are following types byjsu rational numbers.

Its set is represented by are denoted by Z or I. Fractions :. A fraction is part of. A fraction is always positive where as a rational number can be positive or negative.

Ratiobal Numbers:. Its set is represented by N. The number of natural number rrational infinite. The natural numbers are also known as Positive Integers. Whole Numbers:. Its set is represented by W. Thus, N W. The whole numbers are also known as Non-Negative integers. Rational Numbers:. Thus, the set of the rational numbers contains all integers and fractions.

The set of rational numbers is denoted by Q. Therefore, N W Z Q. How do we represent the rational number in decimal form? What mxths the terminating, non-terminating and recurring decimal? Now, in the non-terminating decimal, either the decimal part is repeating, recurring or no repeat, non-recurring. In the division of these rational numbers, we get the remainder zero byjus class 8 maths rational numbers sum a finite steps.

The recurring decimal numbers are also represented as. How do we identify that the fraction is terminating or non-terminating decimal numbers without skm division? In the rational number or fractionif the prime factorization of the denominator q is in the form of 2 m 5 n byjus class 8 maths rational numbers sum, it means, the prime factors of the denominator q are 2 or 5 or.

Otherwise, the fraction is non-terminating decimal. Thus, is non-terminating decimal. How do flass express matbs recurring decimal as fraction? To express the recurring decimal number in a fraction, we use a formula as below. In the following, the number of recurring digits E and F is 2, we write 9 as two times and the number of non-recurring digits D after decimal point is 1, we write 0 as one time.

For example:. How do we compare two or more rational numbers? To compare two or more rational numbers, byjus class 8 maths rational numbers sum do byjus class 8 maths rational numbers sum following steps:. Step 1: Express each of the rational numbers with the positive denominator. Step 2: Find the LCM of these positive denominators. Step 3: Express each of the byjus class 8 maths rational numbers sum number with this LCM as the common ratkonal.

Step 4: The numerator having the greater numerator is greater. Arrange the numbers. Thus, we. How do we represent the rational numbers on number line? Natural Numbers : To represent natural numbers on fational number line, we draw a line and mark natural numbers 1, 2, 3, � on it as. The line extends indefinitely only to the right side of 1. There is no number to the left of 1. Whole Numbers : To represent whole numbers on the number line, we draw a line and mark whole numbers 0, 1, 2, 3, � on it as.

The byjus class 8 maths rational numbers sum extends indefinitely only to the right side of 0. There is no number to the left of 0. Now, we mark 1 and 2 on the number line. How to add two rational numbers if the given rational numbers have same denominator? When the given rational numbers have same denominator, then we use the method as. Add the rational numbers.

How to add two rational numbers if the given rational numbers have different denominator? When the given rational numbers have same denominator, then we take the LCM of their denominators and express each of the given numbers with this LCM as the common denominator. Now, we add these numbers as. Find the sum. The denominator of the given numbers are 6 and 9.

Thus. What are the properties of addition of rational numbers? There are following properties of addition of rational numbers:. Property 1: The sum of two rational numbers is always a rational number. It means, if and are numbers, then are rational number. Property 2: Two rational numbers can be added in any order. Property 3: While adding three rational numbers, they can be grouped in any order.

Property 4: 0 zero is a rational number such that the sum of any rational number and 0 zero is the rational number. How to subtract two rational numbers? Subtract. What are the properties of subtraction of rational number? There nu,bers following properties of subtraction of rational number:.

Property 1: The byjus class 8 maths rational numbers sum of two rational numbers is always a rational number. It means, if and are rational numbers, then � is rational number. Property 2: Two rational numbers cannot be subtracted in any order. Mathss means, if and are numbers, then � �. How do we multiply two rational numbbers For two rational numbers andwe get the multiplication as. We multiply as. What are the properties of multiplication of rational number?

There are following properties ratonal multiplication of rational number:. Property 1: The multiplication or the product of two rational number is always a rational number. It means, if nnumbers are numbers, then is rational number. Property 2: Byjus class 8 maths rational numbers sum rational number can be multiplied in any order.

Property 3: While multiplying three rational numbers, they can be grouped in any order. Property 4: 1 one is a rational number such that the product of any rational number and 1 is the rational number. Note that clsas zero has no reciprocal, because is not defined. The reciprocal of 1 is mathss and the reciprocal of -1 is Property 7: If we multiply any rational number with 0 zerothen the result is always 0 zero.

How do we divide two rational number? Divide by. What are the properties of division of rational number? Eum are following properties of division of rational number:. Property 1: If and are two numbers such that 0, then is also a rational number.

How do we find a rational number between two rational number? Find a rational number between .

Make point:

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This chapter mainly deals with problems based on rational numbers, whole numbers, natural numbers, representation of rational numbers on the number line. In order to help you understand and solve the problems, we, at BYJU�S, have prepared the RD Sharma Class 8 Chapter 1 . NCERT Exemplar Class 8 Maths Chapter 1 Rational Numbers, provided here for students to prepare for exams. These exemplars problems and solutions are designed by experts in accordance with CBSE syllabus() for 8th standard, which covers all the topics of Class 8 Maths Chapter 1. Given, the sum of two rational numbers One of the numbers To find the other number, we need to subtract the first number from the sum. i.e. other rational number. Question 6. Which rational number should be added to. to get? Solution: Required rational number. Taking LCM. 2 9,8 2 9,4 2 9,2 3 9,1 3 3,1 1,1 ?LCM of 9 and 8=2?2?2?3?3=




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