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RS Aggarwal Class 7 Solutions Chapter-4 Rational Numbers

RS Aggarwal Solutions

RS Aggarwal Class 7 Solutions Chapter-4 Rational Numbers

Last updated date: 25th Apr 2024

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Class 7 RS Aggarwal Chapter-4 Rational Numbers Solutions - Free PDF Download

Vedantu provides the solutions of RS Aggarwal Class 7 Math Chapter 4. The topic of Chapter 4 of Mathematics is a Rational Number. The Chapter Rational Number in Class 7 RS Aggarwal deals with the concepts involving the definitions and properties of the rational number. The way the solutions are provided by Vedantu is easily understandable. The stepwise solutions of every sum of the Chapter give the student an enhanced insight into the Chapter. You can download the PDF of the solutions of Chapter 4 for free from Vedantu.

Every NCERT Solution is provided to make the study simple and interesting on Vedantu. Vedantu is No.1 Online Tutoring Company in India Provides you Free PDF download of NCERT Math Class 7 solved by Expert Teachers as per NCERT (CBSE) Book guidelines. All Chapter wise Questions with Solutions to help you to revise complete Syllabus and Score More marks in your examinations. You can also register Online for NCERT Class 7 Science tuition on Vedantu to score more marks in your examination.

Introduction

Rational Numbers

A rational number is one that may be represented in the following way:

x/y, where x and y are integers and y is not equal to 0.
We utilize various quantities in our daily lives that are not whole numbers but can be expressed as fractions p/q. As a result, we require rational numbers.

Rational Numbers with Equivalents

By multiplying or dividing the numerator and denominator of a rational number by the same non-zero integer, we receive another rational number that is equivalent to the original rational number. Equivalent fractions are what they're called.

Standardized Rational Numbers

If the denominator is a positive integer and the numerator and denominator have no common factor other than 1, the rational number is said to be in standard form.

LCM

The smallest number (≠0) that is a multiple of both is the least common multiple (LCM) of two numbers.

Example: LCM of 5 and 6 can be calculated as shown below:

0, 5, 10, 15, 20, 25, 30, 35 are multiples of 5.

0, 6, 12, 18, 24, 30, 36 are multiples of 6.

30 is the L.C.M. of 5 and 6.

Rational Numbers in the Interval Between Two Rational Numbers

Any two rational numbers can have an endless number of rational numbers between them.
List some rational numbers between 35 and 13 as an example.

The L.C.M. of 5 and 3 equals 15.

Rational Numbers and Their Properties

Property of Closure

A rational number is a sum, difference, and product of two rationals. As a result, rational numbers are closed when they are added, subtracted, or multiplied, but not when they are divided.

Property of Commutativity

x*y=y*x for any two rational numbers x and y.
When it comes to addition and multiplication, rational numbers are commutative, but not when it comes to subtraction and division.

Property of Association

(a*b) c=a (b*c) for any three rational numbers a, b, and c.
When it comes to rational numbers, addition and multiplication are associative, but subtraction and division are not.

Reciprocals and Negatives

Positive and negative rational numbers are the two types of rational numbers.

A positive rational number is one in which the numerator and denominator are both positive integers or negative integers.
A negative rational number is one in which either the numerator or denominator is a negative integer.

When the product of two rational integers is 1, they are referred to as each others’ reciprocals.

Note that a rational number's product with its reciprocal is always 1.

We have provided step by step solutions for all exercise questions given in the PDF of Class 7 RS Aggarwal Chapter-4 Rational Numbers. All the Exercise questions with solutions in Chapter-4 Rational Numbers are given below:

At Vedantu, students can also get Class 7 Math Revision Notes, Formula and Important Questions and also students can refer to the complete Syllabus for Class 7 Math, Sample Paper and Previous Year Question Paper to prepare for their exams to score more marks.

RS Aggarwal Solutions Class 7 Chapter 4 (Rational Numbers)

First of all, to attempt to solve the questions of this Chapter a student must know,

What is a Rational Number?

A Rational Number is defined as a number that can be expressed in the form of p/q where q ≠ 0. For example 1/3, 50/34, 72/99, etc. A rational number can be positive, negative, and zero and can also be expressed in the form of a fraction. Therefore, all the whole numbers are rational numbers.

Properties of Rational Number

Closure Property: A+B=B+A

A*B=B*A

Associative Property: A+(B+C)=(A+B)+C

(A*B)*C= A*(B*C)

Distributive Property: A*(B+C)=A*B+A*C

Standard Form of Rational Numbers

A rational number is said to be standard when the denominators and numerators of a rational number have only a common factor of 1.

For example; 24/120, a rational number whose numerator and denominator are 24 and 120 respectively, have more than 1 common factor. Now when 24/48 is simplified, we get ½ which is in standard form. ½ is in standard form since 1 and 2 have no common factor other than 1.

Difference Between Positive and Negative Rational Numbers

Positive Rational Numbers

Negative Rational Numbers

Definition: A Rational number is said to be positive if both the numerator and denominator have the same signs.

Examples: 13/72, 1/4, 25/50

Definition: A Rational number is said to be negative if the numerator and denominator have opposite signs.

Examples : -13/72 , -1/4 , -25/50

Range: Greater than 0

Range: Less than 0

The Multiplicative Inverse of Rational Numbers

The reciprocal of a given rational number is the multiplicative inverse of that rational number. Therefore, the multiplication of the rational number and the multiplicative inverse should always be equal to 1.

Example: Find the multiplicative inverse of 7/23.

Solution:

Reciprocal of 7/23 = 23/7

Now, 7/23*23/7=1

Therefore, 23/7 is the multiplicative inverse of 7/23.

Additive Inverse of Rational Number

The additive inverse of a rational number is the number that when added to the rational number gives zero. Therefore, the additive inverse of a rational number is negative of that rational number.

Example: Find the additive inverse of -4/13.

Solution: Additive inverse = - ( - 4/13) = 4/13

-4/13+4/13=0

Therefore, 4/13 is the additive inverse of -4/13.

Difference Between Rational and Irrational Numbers

Rational Numbers	Irrational Numbers
Definition: A rational number is defined as a number that can be expressed in the form of p/q where q ≠ 0.	Definition: A rational number is defined as a number that cannot be expressed in the form of p/q.
It includes only the decimals that are finite and are recurring.	It includes the number that is non-terminating or non-recurring.
Example: 10/13, 1.4444, 1.12346….	Example: √ 55, √ 5, √ 34

Preparation Tips

First, go through the Chapter thoroughly and cover all the topics.
Note down all the important formulae and try to learn them.
Start solving the exercise questions without any guidance from anyone.
Try the questions at least 3 times if you are unable to solve them.
Seek help from Vedantu’s solution to check your answers and solve the ones that you were unable to solve.

FAQs on RS Aggarwal Class 7 Solutions Chapter-4 Rational Numbers

1. Should I Refer to Vedantu’s Solution for Getting a Good Score in School Exams?

Yes, without any second thought follow Vedantu’s solutions. The solutions are prepared by Vedantu’s top educators based on the current guidelines of the CBSE. It is prepared as per the understanding of all types of students.

Even if you are an average or a below-average Math student, if you know the outline of the Chapter you will understand all the solutions with great ease. Moreover, if you follow Vedantu’s solution, you will surely see positive results in your school exams. Since the solutions are shown in a step by step manner, it helps the students to clear their concept regarding a particular topic.

2. Why Should I Study RS Aggarwal Solutions Class 7 Chapter 4- Rational Numbers from Vedantu? How Reliable is Vedantu?

Vedantu covers all the topics that are asked in an exam. The study material is suited for students of different intellect. It helps the students in developing a deep understanding of the topic which will help them significantly in higher education. The study material is prepared in a way that clarifies all the major doubts that a student may incur initially while learning RS Aggarwal solutions Class 7 Chapter 4 (Rational Numbers).

3. How to add rational numbers following the concepts of RS Aggarwal Class 7 Chapter 4?

Addition of two rational numbers with the same denominators: Add the numerators of two rational numbers with the same denominators while keeping the denominator the same.

Two rational numbers with distinct denominators are added: We start by finding the LCM of the two denominators, just like we did with fractions. Then, using this LCM as the denominator, we get the rational numbers that are comparable to the supplied rational numbers. Now, as in, we add the two rational numbers together (A).

4. Following the concepts of RS Aggarwal Class 7 Chapter 4, how to compare rational numbers?

There can be three situations for the comparison of rational numbers; between positive rational numbers, between negative rational numbers, and between a positive and a negative rational number.

Two positive rational numbers can be compared in the same way that two fractions can be compared.
By disregarding their negative signs and then reversing the order, two negative rational numbers can be compared.
The difference between a negative and a positive rational number is self-evident since a negative rational number is always smaller than a positive rational number.

5. What is the difference between positive and negative rational numbers, according to RS Aggarwal Class 7 Chapter 4?

If the numerator and denominator of a rational number are both positive, it is said to be positive. A positive rational number is one in which the numerator and denominator of a rational number are both positive integers or both negative integers.

Negative rational numbers have a numerator that is a negative integer and a denominator that is a positive integer. Similarly, is a negative rational number if the numerator is a positive integer and the denominator is a negative integer.