NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers all exercises in Hindi and English medium PDF format. It is updated for the new academic year 2022-2023. NCERT Textbook solutions are useful for both UP Board (High School) Schools, and CBSE Board Schools.

• ## 10th Maths Chapter 1 Exercise 1.4

### NCERT Solutions for Class 10 Maths Chapter 1

Uttar Pradesh Board is now following NCERT Books for 2022-23. So, students can download UP Board Solutions for Class 10 Maths Chapter 1 from this page. Download Class 10 Maths App or Class 10 Ganit App or Offline Apps for other subjects for offline use in UP Board or CBSE or other boards based on NCERT Book’s Syllabus. Visit Discussion Forum to share your knowledge and ask your doubts. In Chapter 1 of 10th Maths, we observe that Euclid’s division algorithm has to do with divisibility of integers. The result obtained from Euclid’s Lemma is quite easy to state and understand. In Class 10 Maths, there are many applications related to the divisibility properties of integers. Here, we will try a few of them to compute the HCF of two positive integers.

 Class: 10 Maths (English and Hindi Medium) Chapter 1: Real Numbers

### 10th Maths Chapter 1 Solutions

Class 10 Maths Chapter 1 NCERT Solutions 2022-23 and study material related to 10th Maths chapter 1 is modified according to latest CBSE Syllabus 2022-2023. UP Board students also use this solution for their exams. The fundamental theorem of arithmetic and Euclid’s division lemma are the main topics of this chapter (Real Numbers). The Fundamental Theorem of Arithmetic and Euclid’s division lemma has many applications, both within mathematics and in other fields. NCERT Solutions of all other subjects are also available in PDF form.

#### Changes in CBSE Syllabus 2022-2023 Class 10 Maths Chapter 1

Get the latest CBSE syllabus to observe the changes due to corona-virus with full detail for class 10 Maths Chapter 1. CBSE has issued a new syllabus for session 2022-2023 educational session. See all the changes made for Class 10 Maths Syllabus for 2022-2023.

#### Class 10 Maths Chaper 1 Exercise 1.1 and 1.2 Solution in Hindi

Class 10 Maths Chaper 1 Exercise 1.1 Solution in Hindi
Class 10 Maths Chaper 1 Exercise 1.2 Solution in Hindi

#### Class 10 Maths Chaper 1 Exercise 1.1 and 1.2 Solution in Hindi

Class 10 Maths Chaper 1 Exercise 1.3 Solution in Hindi
Class 10 Maths Chaper 1 Exercise 1.4 Solution in Hindi

## Difference between algorithm and lemma.

### Algorithm

An algorithm is a series of well defined steps which gives a procedure for solving a type of problem.

### Lemma

A lemma is a proven statement used for proving another statement.

### Class 10 Maths Chapter 1: Real Numbers

#### Class 10 Maths Exercise 1.1

In Exercise 1.1 of Class 10 Maths Chapter 1, there are only five questions. All the questions are based on Euclid’s Division Lemma and its applications. In Questions number 1 we have to find HCF applying Euclid’s Division Lemma. In Questions number 2, 4 and 5 also apply step by step Euclid’s Division Algorithms to prove the questions. In Questions 3, we have to find out the maximum number of columns in which they can march, that is, HCF of the two numbers.

#### Class 10 Maths Exercise 1.2

In Exercise 1.2 of Class 10 Maths, the Fundamental Theorem of Arithmetic is main to solve the questions. Question number 1, 2, 3 are based on the prime factorisation method of LCM and HCF. In Question 4, we can use direct formula a × b = LCM × HCF. Question number 6 is an important question as per exams point of view and based on Example Number 5. One can solve Question 6 by taking common or directly solving each number and showing that it has more than two factors. At last in Question 7, we have to find out a number which is divisible by both 12 and 18 that is LCM of the two numbers.

#### Class 10 Maths Exercise 1.3

In Exercise 1.2 of Class 10 Maths, only three questions are there. We know that the square root of a non-perfect square number is an irrational number. Here, we have to prove the same fact with a various set of numbers. In each of these questions, first of all, we assume that the given number is a rational number with numerator and denominator as coprime integers. Later on, we receive a false result due to the wrong assumption, so we conclude that the given number is irrational.

#### Class 10 Maths Exercise 1.4

Class 10 Maths Exercise 1.4 deals with that decimal representation of rational numbers. Questions of Exercise 1.4 are based on Theorem 1.5, Theorem 1.6 and Theorem 1.7 given in NCERT Book of Class 10 Maths Chapter 1. Using these theorems, we can find whether the given rational number is either terminating or non-terminating repeating or non-terminating non-repeating. Most often, one mark questions are asked in CBSE Board exams or school tests also from Exercise 1.4 of Class 10 Maths.

#### Euclid’s division algorithm

The step by step way to find the HCF of two positive integers, say c and d, with c > d.

• Step 1: Apply Euclid’s division lemma, to c and d. So, we find whole numbers, q and r such that c = dq + r, 0 £ r < d.
• Step 2: If r = 0, d is the HCF of c and d. If r ≠ 0, apply the division lemma to d and r.
• Step 3: Continue the process till the remainder is zero. The divisor at this stage will be the required HCF.

#### Test & Assignments

Download the practice test series with answers. Level 1 Test 1 contains basic questions for practicing the chapter Real Numbers. Most of the questions of Level 1 Test 2 are easy to understand and provides good practice. Answers of these test series will be available on website free to use.

##### Historical Facts on Real Numbers

The word algorithm come from the name of the name of the 9th century Persian mathematician al-Khwarizmi. The word ‘algebra’ is derived from a book, he wrote, called Hisab al-jabr w’al-muqabala.
An equivalent version of Fundamental theorem of Arithmetic was probably first recorded as Proposition 14 of Book IX in Euclid’s Elements, before it came to be known as the Fundamental Theorem of Arithmetic.
However, the first correct proof was given by Carl Friedrich Gauss in his al-Khwarizmi.
Carl Friedrich Gauss is often referred to as the ‘Prince of Mathematicians’ and is considered one of the three greatest mathematicians of all time, along with Archimedes and Newton. He has made fundamental contributions to both mathematics and science.

###### Prove that the square of an integer is of the form 9k or 3k + 1. ### How to prepare Class 10 Maths Chapter 1 for Exams?

Class 10th Mathematics chapter 1 is much more than real numbers. NCERT solutions include shapes, logic, symbols, and vast varieties of thinking and acknowledging precision. The most usual numbers that we see in everything are natural numbers. These number starts from 1, 2, 3. . . and goes on and on. But if these numbers start from 0 instead of 1 then they will be known as whole numbers. Most of the students in class 10th might find the easy definition complex just because of the inefficient explanation. At Tiwari Academy, we try to change the perception of all the students, who thinks Maths is difficult. Learn the ways to prepare 10th Maths Chapter 1 in easy ways.

#### Step 1: Use of progressive practice method to retain the knowledge. In Chapter 1 of class 10th Maths, you will get an introduction that include irrational numbers, Real numbers and sets of integers. Try the sums to practice yourself by understanding the concepts. Students should download the NCERT Solution for class 10 Maths. You may take the help of other helping books and NCERT school textbooks. We analyzed the books, and found the casting of explanations is motivated by Daily life problems. The problems are helpful in higher education also. Along with grounded in the algebraic construction of the field of real numbers. Learning varieties of numbers is known as progressive practice. Progressive practice is helpful in comparing, measuring, and solving equations. Using progressive practice for each exercises of chapter 1 in 10th Math, the preparation for your board exams will be better. Students should read the introduction to the chapter as early as possible. Jumping to solve the exercises will increase confusion.

#### Step 2: Focus of main formulae and Vocabulary of chapter. Vocabulary is important when learning the real number system. The progression of standards is pretty clear. Each academic year students are expected to learn one new word. This is the reason why glossary is important. Experts suggest pushing the learning process, so students must make the definition themselves. NCERT Class 10th Maths book used visual representation in every topic. The purpose of the images is to make a meaningful definition. Take the help of examples and try to solve each question yourself. Focus on the real-life application in the form of illustration. Looking at illustrations you can summarize the information. Writing this information will help you retain the knowledge of real numbers.

#### Step 3: Be creative in Maths and use the creative examples of 10th Maths Chapter 1. Students of class 10th might struggle to grasp the terms. Our media explanation for the concepts includes a Venn diagram, funnel diagram and video explanation. Diagrams in the videos show concepts of the Natural, Whole, Integers, and, irrational numbers works. Hindi and English Medium videos teach students to simplify the questions, before they classify in the real number system. Fractions are a great example of this chapter, if students are well versed with the operation of rational numbers. They must know about the properties of a rational number. Because rational numbers can be written as p/q format. Learning the concepts from our video lesson helps the students to be more creative. The best part of it is that these premium knowledge is available for free.

#### Step 4: Take help from Hindi and English Medium solutions PDF or Videos. Complex numbers sometimes mark the END of numbers. Despite the fact mathematicians generally present numbers in unique ways. The number can be abstracted in various ways. This includes mathematical units like matrices and sets. Tiwari Academy helps the students to understand all the topics that are challenges the student’s fundamental thinking ability. If you try to understand the ways mathematician present their questions, it would make you comfortable to understand the questions from their perspective. Take help from solutions given here that is available in Hindi and English Medium PDF or Videos. Class 10 Math Chapter 1 makes you deal with lots of cognitive facts about the Real Numbers. We prefer making students more confident while reading questions.

#### Step 5: Give more time to practice exercises of chapter 1 and make space for curiosity. The study says, more than sixty-six percent of students agreed, that if you do want to do well in numbers. Paying attention is not the only thing you do in class. Seek clarification when you need better understanding. To make the practice better you can always go to the discussion. There are many things related to Euclid’s Lemma to learn first and then go form practice. Curiosity is only possible when you work hard to understand the concept of real numbers rather than merely memorizing them. Previously we have mentioned how the NCERT explanation of topics is real-life-based. At Tiwari Academy, We try to cast our explanation that can solve real-world problems. So, you can relate the concept to the real world, which will raise your interest in it.

### How many exercises, questions and examples are there in class 10 Maths chapter 1 Real numbers?

There are 4 exercises in class 10 chapter 1 (Real numbers):
In first exercise (Ex 1.1), there are 5 questions.
In second exercise (Ex 1.2), there are 7 questions.
In third exercise (Ex 1.3), there are 3 questions.
In fourth exercise (Ex 1.4), there are 3 questions.
So, there are in all 18 questions in class 10 chapter 1 (Real numbers).
There are in all 11 examples in class 10 chapter 1 (Real numbers).

• Examples 1,2,3,4 are based on Ex 1.1.
• Examples 5,6,7,8 are based on Ex 1.2.
• Examples 9, 10, 11 are based on Ex 1.3.

### Are there any Theorems or Algorithm in 10th Maths chapter 1?

Yes, there are 7 Theorems and 1 Algorithm in class 10 chapter 1 (Real numbers).
First exercise (Ex 1.1) is based on Theorem 1.1 (Euclid’s Division Lemma) and Euclid’s Division algorithm.
Theorem 1.2 (Fundamental Theorem of Arithmetic) is used in second exercise (Ex 1.2).
Theorem 1.3 and Theorem 1.4 plays important role in third exercise (Ex 1.3).
Last exercise that is Ex 1.4 is based on Theorems 1.5, 1.6, 1.7.

### What are the Important questions from Maths class 10 chapter 1 Real numbers?

Important questions from Maths class 10 chapter 1:

• In first exercise (Ex 1.1), all questions are important.
• In second exercise (Ex 1.2), Q2, 4, 5, 7 are important.
• In third exercise (Ex 1.3), all questions are important.
• In fourth exercise (Ex 1.4), Q1 and Q2 are important.

### Which topics students should recall before starting class 10 Maths chapter 1?

Students should recall some topics of class 9 chapter 1 (Number systems).
Topics:

1. Types of numbers (Natural number, Whole number, Integers, Rational numbers, Irrational numbers and Real numbers).
2. Decimal expansion of Rational numbers (Terminating and Non-terminating recurring) and Irrational numbers (Non-terminating non-recurring).
3. HCF (Highest Common Factor) and LCM (Lowest/Least Common Multiple).
4. And some other topics like Meaning of Dividend, Divisor, Quotient and Remainder, Prime numbers, Composite numbers, Factors.                          