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# NCERT Solutions for class 9 Maths Chapter 1 Exercise 1.4 Number Systems - PDF Download

Class 9 Rational numbers obey the laws of commutativity, associativity, and distribution when it comes to addition and multiplication. if you add, subtract, multiply, or divide two rational numbers, you'll still end up with a rational number. NCERT solutions for class 9 maths chapter 1 ex 1.4 Number Systems explains how irrational numbers follow all the laws mentioned above. The only exception to this rule is that the outcome of addition, subtraction, multiplication, etc. does not necessarily lead to an irrational number.

The NCERT chapter 1 ex 1.4 class 9 maths solutions based on the concepts of operations on real numbers is composed of five questions, which are available in a PDF format on the eSaral website. Class 9 maths chapter 1 exercise 1.4 NCERT solutions are created by subject experts to assist students in preparing for the exam. eSaral provides a comprehensive solution to chapter 1 ex 1.4, of class 9 maths. These are available for free download in PDF format.

## Topics Covered in Exercise 1.4 class 9 Mathematics Questions

In class 9 maths, NCERT solutions for ex 1.4 specifically defined the category of numbers as being rational and irrational by using operations on real numbers.

 1 Operations on Real Numbers
1. Operations on Real Numbers

When dealing with real numbers and the mathematical operations on them, you should keep in mind the following pointers:

• The sum or difference of a rational number and an irrational number is irrational.

• The product or quotient of a non-zero rational number with an irrational number is irrational.

• If we add, subtract, multiply or divide two irrationals, the result may be rational or irrational.

If a and b be positive real numbers, then we have:

1. √ab = √a √b

2. √a/b =  √a/√b

3. (√a + √b)(√a – √b) = a – b

4. (a + √b)(a – √b) = a2 – b

5. (√a + √b)(√c + √d) = √ac + √ad + √bc + √bd

6. (√a + √b)2 = a + 2√ab + b

## Tips for Solving Exercise 1.4 class 9 chapter 1 Number Systems

NCERT solutions class 9 maths chapter 1 ex 1.4 helps the students to learn how to do the operation on real numbers.

1. It would be helpful if you revise the concepts of operations on real numbers.

2. NCERT solutions class 9 maths chapter 1 ex 1.4 conveys the concepts of the number system in such a way that it builds a solid basis of mathematical knowledge, and of course, increases your confidence in learning this topic.

3. You must remember the identities related to real numbers to solve ex 1.4 questions with ease.

## Importance of Solving Ex 1.4 class 9 Maths chapter 1 Number Systems

NCERT solutions class 9 maths chapter 1 ex 1.4 discusses the topic related to operations on real numbers which is an important part of this exercise. Here are some of the advantages of solving ex 1.4.

1. NCERT solutions for class 9 maths ex 1.4 helps you to create fundamental concepts about  operations on real numbers.

2. By solving NCERT solutions for class 9 maths chapter 1 ex 1.4, it builds a solid base of mathematical skills and, of course, increases your confidence in learning new concepts in upper classes.

3. This exercise 1.4 in class 9 maths will help us to learn how to do operations on real numbers. This exercise may help you to solve the questions in ex 1.4 in simple steps.

4. Our experienced teachers will provide you with step-by-step strategies to ensure you perform well on your final exams.