RS Aggarwal Class 8 Chapter 1 Solutions (Rational Numbers)
RS Aggarwal Class 8 Maths Solutions Chapter 1 ‘Rational Numbers’ are the best study material to enhance your understanding of this chapter. In this chapter of RS Aggarwal Class 8 Maths Solutions, you will revise the concepts of expressing integers as rational numbers, properties of rational numbers, the inverse of rational numbers, the order of rational numbers and equality of rational numbers. There are 9 exercises in the chapter with 118 questions.
As you will practice the RS Aggarwal Class 8 Maths Chapter 1 problems, you will gain confidence in solving any kinds of problems related to Rational Numbers. You will be familiar with all the concepts of the chapter. Our Maths subject matter experts have created exercise-wise solutions for RS Aggarwal Class 8 Chapter 1 to provide you with the right help if you get stuck while practising the questions.
Our subject matter experts adhere to the latest CBSE guidelines for Class 8 Maths and have solved each question stepwise. You will also find proper reasoning along with every solution. Given below are some important topics related to the chapter that will help you in revising the concepts easily. Then, we have also provided exercise discussion for RS Aggarwal Class 8 Chapter 1 solutions.
Important Topics for RS Aggarwal Class 8 Maths Solutions Chapter 1: Rational Numbers
Natural Numbers, Whole Numbers and Integers
Before you solve the RS Aggarwal exercises for Class 8 Chapter 1, you must understand what are Natural Numbers, Whole Numbers and Integers. All the positive countable numbers are called natural numbers, however, it does not include zero. All the natural numbers and zero altogether are called whole numbers. Then, all the positive and negative numbers along with zero are grouped together as integers.
When a number is expressed as the ratio of two integers, it is called a rational number. For instance, ½, -½, ¾, -2/19, all are rational numbers. Here, the denominator cannot be zero.
Properties of Rational Numbers
- Closure Property: When an arithmetic operation is applied to two rational numbers, the result is also a rational number. Rational numbers are closed under addition, subtraction and multiplication but not under division.
For example: 4/5 + 3/5 = 7/5, where 4/5, 3/5 and 7/5 are all rational numbers.
Similarly, 4/5 – 3/5 = 1/5, where 4/5, 3/5 and 1/5 are all rational numbers.
4/5 x 3/5 = 12/25, where 4/5, 3/5 and 12/25 are all rational numbers.
But, 4/5 0= ∞, where 4/5, and 0 are all rational numbers but, ∞ is not a rational number.
- Commutative Property: When we swap two rational numbers between any given arithmetic operator and the result of the expression remains the same. Rational numbers are commutative under addition and multiplication but not under subtraction and division.
For example: 4/5 + 3/5 = 7/5, and 3/5 + 4/5 = 7/5
Similarly, 4/5 x 3/5 =12/25, and 3/5 x 4/5 = 12/25
But, (4/5) / (3/5) = 4/3, and (3/5) / (4/5) = 3/4, so rational numbers are not commutative under division.
- Associative Property: When we swap the places of rational numbers between two or more same type of arithmetic operators and the result remains the same. Rational numbers are associative under addition and multiplication but not under subtraction and division.
For example: 4/5 + (3/5 + 2/5)= 9/5, and (4/5 + 3/5) + 2/5 = 9/5,
But, 4/5 – (3/5 – 2/5)= 3/5, and (4/5 – 3/5) – 2/5 = -1/5
The Inverse of Rational Numbers
A rational number can have two types of inverse operations. Additive inverse, where the inverse of rational number ‘m/n’ will be -(m/n) and multiplicative inverse, where the inverse of a rational number ‘m/n’ will be (n/m).
Exercise Discussion for RS Aggarwal Class 8 Maths Solutions Chapter 1: Rational Numbers
- In exercise 1A of RS Aggarwal Solutions for Class 8 Maths Chapter 1, there are multiple-choice questions based on the standard form of rational numbers, arranging rational numbers in ascending and descending order and comparison of rational numbers. There are also state true or false questions based on number systems.
- In exercise 1B you have to represent the given rational numbers on a number line.
- In exercise 1C there are questions related to addition and subtraction of rational numbers and the additive inverse of rational numbers. There are fill in the blanks type questions based on the properties of rational numbers.
- Exercise 1D includes questions on multiplication of rational numbers. There are questions where you have to prove that LHS is equivalent to the RHS. Some questions are based on the multiplicative inverse of rational numbers.
- In exercise 1E you have to simplify the given rational numbers. There are questions related to the division of rational numbers and the properties of the division of rational numbers.
- In exercise 1F you have to find a rational number between two given rational numbers.
- Exercise 1G is slightly different and tough as it contains word problems based on the application of rational numbers.
- Exercise 1H is a miscellaneous exercise that includes questions on all the topics discussed in the other exercises. You will be able to revise all the concepts here.
Benefits of Instasolv’s RS Aggarwal Class 8 Maths Solutions Chapter 1: Rational Numbers
- You can easily practice the concepts of rational numbers such as the four important properties of rational numbers, representing rational numbers on a number line etc. with the help of our RS Aggarwal Class 8 Maths Solutions for Chapter 1.
- Our solutions act as a guide that would save your time as you will be able to resolve your problems related to the exercises of RS Aggarwal Chapter 1 on your own.
- It is a great opportunity to learn independently and gain confidence in solving questions in the exams.
- If you have any further questions, you can send us your queries any time and get instant solutions from our subject matter experts.