# NCERT Solutions Class 10 Maths Chapter 1 Real Numbers

NCERT solutions for class 10 maths Chapter 1 Real Numbers encompasses essential concepts around real numbers such as Euclid’s division lemma, Prime Numbers, Composite Numbers, Fundamental Theorem of Arithmetic, HCF, and LCM by Prime Factorization Method, and Irrational Numbers. Real numbers are the combination of rational and irrational numbers. They are denoted by the symbol "R" and can be both positive and negative. NCERT solutions class 10 maths Chapter 1 will help cover all the relevant concepts of real numbers as it has significant applications in real life. Kids also learn about important facts such as the use of the Fundamental Theorem of Arithmetic in proving the irrationality of many of the numbers and exploring when exactly the decimal expansion of a rational number is terminating and when it is non terminating. As numbers form the foundation of Mathematics, understanding the basics is a must.

In this chapter, students will also learn how to represent the real numbers on a number line and the process of successive magnification, which is used to represent a decimal expansion on a number line. The lesson combines certain concepts that kids have come across in previous classes with newer complicated topics to give them a holistic understanding of real numbers and their application. The Class 10 Maths NCERT Solutions Chapter 1 can be found in the pdf format below and also you can find some of these in the exercises given below.

- NCERT Solutions Class 10 Maths Chapter 1 Ex 1.1
- NCERT Solutions Class 10 Maths Chapter 1 Ex 1.2
- NCERT Solutions Class 10 Maths Chapter 1 Ex 1.3
- NCERT Solutions Class 10 Maths Chapter 1 Ex 1.4

## NCERT Solutions for Class 10 Maths Chapter 1 PDF

Mathematics presents us with a variety of numbers and real numbers are one of them. In order to understand higher mathematics, it makes sense to first take a look at the number system in detail which has been achieved in this book. An interesting aspect of the NCERT book is that it details some historical notes, cutting the monotony of studies. Further, the solutions have certain tips and tricks to help a child streamline his process of learning. The links for NCERT Solutions Class 10 Maths available for free PDF download are given below:

**ā** Download Class 10 Maths NCERT Solutions Chapter 1 Real Numbers

**NCERT Class 10 Maths Chapter 1 **

### NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers

With the aid of the easily available links above, students will get to explore real numbers with a variety of examples and problems. It is essential to read the theorems and explanations first before moving on to the solved examples and exercise questions. Kids should make it a point to periodically revise these links as some questions can prove to be confusing. Thus, if not given ample time to study students might not be able to recall concepts when required. The exercise-wise analysis of NCERT Solutions Class 10 Maths Chapter 1 Real Numbers is given below :

- Class 10 Maths Chapter 1 Ex 1.1 - 5 Questions
- Class 10 Maths Chapter 1 Ex 1.2 - 7 Questions
- Class 10 Maths Chapter 1 Ex 1.3 - 3 Questions
- Class 10 Maths Chapter 1 Ex 1.4 - 3 Questions

**Topics Covered**: The topics covered in Class 10 maths NCERT solutions Chapter 1 are Euclid’s division algorithm, the Fundamental Theorem of Arithmetic, revision of Irrational Numbers & Rational Numbers, Prime Numbers, Composite Numbers, HCF, and LCM by Prime Factorization, as well as proving if a number is rational or irrational. All the questions related to these topics are discussed in detail in the NCERT solutions.

**Total Questions**: Class 10 maths chapter 1 Real Numbers consists of 18 key questions, of which 10 are easy, 5 are moderate, and 3 are complicated sums. By solving the problems, students can cover all the topics of this chapter and prepare for their board exams.

## List of Formulas in NCERT Solutions Class 10 Maths Chapter 1

NCERT solutions Class 10 maths chapter 1 covers the formulas based on the properties of real numbers and their theorems. These formulas will help the students solve questions accurately and quickly. They are not just helpful for class 10, but higher-level mathematics as well. Apart from these, it is necessary for kids to remember certain points related to a particular category of numbers. For example, the decimal expansion of an irrational number is non-terminating and non-repeating. Let us go through some of the formulas and properties covered in NCERT Solutions Class 10 Maths Chapter 1 Real Numbers:

- Commutative Property: m + n = n + m
- Associative Property: m + (n + r) = (m + n) + r
- Euclid’s Division Lemma: [a=bq+r,0≤r<b]

## FAQs on NCERT Solutions Class 10 Maths Chapter 1

### Why are NCERT Solutions Class 10 Maths Chapter 1 vital for scoring well?

NCERT Solutions Class 10 Maths Chapter 1 deals with real numbers and their concepts which strengthens the student’s theoretical and practical knowledge. This chapter helps kids understand the divisibility and multiplication of integers through concepts like Euclid’s Division Lemma and the Fundamental Theorem of Arithmetic. These concepts have deep and significant applications as well as carry a good weightage in board exams. Thus, the NCERT solutions class 10 Maths Chapter 1 is vital for the students to score well.

### Do I Need to Practice all Questions Given in NCERT Solutions Class 10 Maths Real Numbers?

We have a total of 18 questions in NCERT solutions class 10 maths Real Numbers which are in various formats. Some of the questions related to topics like LCM and HCF, prime factorization, need a step-wise approach. Euclid’s Division Lemma is one topic that requires regular practice. Since all the questions cover a variety of topics, you must practice each and every question of this chapter.

### What are the Important Topics Covered in NCERT Solutions Class 10 Maths Chapter 1?

The important sub-topics covered in NCERT Solutions Class 10 Maths Chapter 1 are Euclid’s Division Lemma and the Fundamental Theorem of Arithmetic. Euclid’s Division Lemma helps students calculate the HCF of two positive integers while the Fundamental Theorem of Arithmetic is useful in finding the HCF and LCM of two positive integers. Students can practice questions related to both topics in order to get a crystal-clear understanding of the subject matter.

### How Many Questions are there in NCERT Solutions Class 10 Maths Chapter 1 Real Numbers?

There are a total of 18 well-researched questions in the NCERT Solutions Class 10 Maths Chapter 1 Real numbers. These 18 questions are accurately placed to match the context of the theory. They are divided into 4 exemplar exercises. The 18 questions are further segregated into long answers, moderate level, and easy ones. Students can allocate sufficient time to each of these subcategories to gain mastery of this topic.

### What are the Important Formulas in NCERT Solutions Class 10 Maths Chapter 1?

The important formulas mentioned in the NCERT Solutions class 10 maths chapter 1 are the properties of real numbers like commutative and distributive properties, the equation for Euclid’s Lemma, and its proof. These formulas have frequent applications in the chapter and are very easy to remember. Therefore, students must read the theory and understand the derivation of these formulas.

### Why Should I Practice NCERT Solutions Class 10 Maths Real Numbers Chapter 1?

Consistent practice can do wonders. NCERT Solutions helps the students to be confident and solidify their mathematical knowledge. Understanding concepts like rational numbers, irrational numbers, HCF, LCM will assist the kids in preparing for higher classes. Hence, practicing the NCERT Solutions Class 10 Maths Real Numbers Chapter 1 is essential for 10th-grade students.