NCERT Exemplar Class 9 Maths Solutions Chapter 1 Number Systems – Infinity Learn

# NCERT Exemplar Class 9 Maths Solutions Chapter 1 Number Systems – Infinity Learn

NCERT Exemplar Class 9 Maths Solutions Chapter 1 Number Systems are created by a skill ful faculty at Infinity Learn. These Solutions of NCERT Maths help the Learner in solving the issues adroitly and efficiently for the first term. They also concentrate on formulating the solutions of Maths in such a way that it is easy for the students to comprehend and gain in depth knowledge. The NCERT Exemplar Class 9 Maths Solutions goal is to give students detailed and step-wise process for all the answers to the questions given in the exercises of this Chapter.

In NCERT Exemplar Solutions, students are introduced to topics that are considered to be very important for those who wish to pursue Mathematics as a subject in their higher classes. Based on these NCERT Exemplar Solutions, students can practise and prepare for their upcoming first term exams, as well as prepare themselves with the basics of Class 10 for the term wise exams then. These Maths Solutions of NCERT Class 9 are helpful as they are prepared with focus to the latest update on CBSE syllabus for 2024-25 and its guidelines.

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## NCERT Exemplar Class 9 Maths Chapter 1 – Free PDF Download

The NCERT Exemplar Class 9 Maths Chapter 1, “Number System,” covers a fundamental concepts in mathematics. Here, students learn about rational and irrational numbers, decimal expansions, operations on real numbers, laws of exponents, and more. To help in thorough preparation, exemplar problems and solutions have been designed by experts to align with the CBSE Syllabus for Class 9. Download the Chapter wise NCERT Exemplar Maths Class 9 PDF here along with CBSE maths notes class 9.

### NCERT Exemplar Class 9 Maths Chapter 1 Questions with Answers

Question 1: Find the value of x if 3x + 2 = 17.

Answer: To find the value of x, we need to solve the equation 3x + 2 = 17.

Step 1: Subtract 2 from both sides of the equation.

3x + 2 – 2 = 17 – 2

3x = 15

Step 2: Divide both sides of the equation by 3.

3x/3 = 15/3

x = 5

Therefore, the value of x is 5.

Question 2: Simplify: (√25 × √16) ÷ √100

Answer: To simplify the expression, we need to use the properties of square roots.

Step 1: Simplify the numerator.

√25 × √16 = √(25 × 16) = √400 = 20

Step 2: Simplify the denominator.

√100 = 10

Step 3: Divide the numerator by the denominator.

(√25 × √16) ÷ √100 = 20 ÷ 10 = 2

Therefore, the simplified expression is 2.

Question 3: Rationalize the denominator of the fraction: 3/(√2 – 1)

Answer: To rationalize the denominator, we need to multiply both the numerator and denominator by a suitable number to eliminate the square root.

Step 1: Multiply both the numerator and denominator by (√2 + 1).

3/(√2 – 1) = (3 × (√2 + 1))/(√2 – 1) × (√2 + 1)

Step 2: Simplify the numerator and denominator.

(3 × (√2 + 1))/(√2 – 1) × (√2 + 1) = (3√2 + 3)/(2 – 1) = (3√2 + 3)/1 = 3√2 + 3

Therefore, the rationalized denominator is 3√2 + 3.

Question 4: Classify the following numbers as rational or irrational:

a) √9

b) 0.333…

c) 5/7

d) √2

a) √9 = 3 (rational)

b) 0.333… = 1/3 (rational)

c) 5/7 (rational)

d) √2 (irrational)

Question 5: Solve the following inequality: 2x + 5 < 13

To solve the inequality 2x + 5 < 13:

Step 1: Subtract 5 from both sides.

2x < 8

Step 2: Divide by 2.

x < 4

Therefore, the solution to the inequality is x < 4.

Question 6: Find the HCF of 72 and 120 using the prime factorization method.

Step 1: Find the prime factors of 72 and 120.

72 = 2^3 × 3^2

120 = 2^3 × 3 × 5

Step 2: Identify the common factors and multiply them.

HCF(72, 120) = 2^3 × 3 = 24

Question 7: Express 0.6 as a fraction in simplest form.

To express 0.6 as a fraction:

0.6 = 6/10 = 3/5

Therefore, 0.6 as a fraction in simplest form is 3/5.

Question 8: Determine whether the following statements are true or false:

a) Every natural number is a whole number.

b) Every whole number is a natural number.

c) Every integer is a rational number.

a) True

b) True

c) True

Question 9: Solve the following equation for x: 2(x + 3) = 10

To solve the equation 2(x + 3) = 10:

Step 1: Distribute the 2 on the left side.

2x + 6 = 10

Step 2: Subtract 6 from both sides.

2x = 4

Step 3: Divide by 2.

x = 2

Therefore, the solution to the equation is x = 2.

Question 10: Simplify the expression: √18 + √32

To simplify the expression √18 + √32:

Step 1: Find the prime factorization of 18 and 32.

√18 = √(2 × 3^2) = 3√2

√32 = √(2^5) = 4√2

Step 2: Substitute the simplified forms back into the expression.

√18 + √32 = 3√2 + 4√2 = 7√2

Therefore, the simplified expression is 7√2.

Question 11: Determine the value of ‘p’ if 5p – 3 = 22.

To find the value of ‘p’ in the equation 5p – 3 = 22:

Step 1: Add 3 to both sides of the equation.

5p = 25

Step 2: Divide by 5 to solve for ‘p’.

p = 5

Therefore, the value of ‘p’ is 5.

Question 12: Find the LCM of 12 and 15 using the prime factorization method.

Step 1: Find the prime factors of 12 and 15.

12 = 2^2 × 3

15 = 3 × 5

Step 2: Identify the common and uncommon factors.

LCM(12, 15) = 2^2 × 3 × 5 = 60

Therefore, the LCM of 12 and 15 is 60.

Question 16: Express 0.75 as a fraction in simplest form.

To express 0.75 as a fraction:

0.75 = 75/100 = 3/4

Therefore, 0.75 as a fraction in simplest form is 3/4.

Question 17: Determine whether the following statements are true or false:

a) Every integer is a whole number.

b) Every whole number is a natural number.

c) Every rational number is an integer.

a) True

b) True

c) False

Question 18: Solve the following equation for x: 4(x – 2) = 12

To solve the equation 4(x – 2) = 12:

Step 1: Distribute the 4 on the left side.

4x – 8 = 12

Step 2: Add 8 to both sides.

4x = 20

Step 3: Divide by 4 to solve for ‘x’.

x = 5

Therefore, the solution to the equation is x = 5.

Question 19: Find the LCM of 18 and 24 using the prime factorization method.

Step 1: Find the prime factors of 18 and 24.

18 = 2 × 3^2

24 = 2^3 × 3

Step 2: Identify the common and uncommon factors.

LCM(18, 24) = 2^3 × 3^2 = 72

Therefore, the LCM of 18 and 24 is 72.

### Find the Detailed overview of the topics covered within Chapter 1

Rational Numbers and Irrational Numbers

Understanding the properties and distinctions between rational and irrational numbers.
Exploring their representations on the number line.

Finding Rational Numbers Between Two Given Numbers

Employing techniques to determine rational numbers lying between specified intervals.

Locating Irrational Numbers on a Number Line

Developing skills to identify irrational numbers within a given range.

Real Numbers and Their Decimal Expansions

Analyzing the nature of decimal expansions, discerning between terminating, non-terminating, recurring, and non-recurring decimals.

Finding Irrational Numbers Between Two Given Numbers

Utilizing methods to discover irrational numbers situated between defined bounds.

Operations Performed on Real Numbers

Mastering addition, subtraction, multiplication, and division of real numbers.
Understanding the properties of these operations and their applications.

Rationalizing the Denominator

Learning techniques to rationalize denominators involving radicals or irrational expressions.

Laws of Exponents for Real Numbers

Exploring the fundamental laws governing exponentiation in the realm of real numbers.

To facilitate effective learning and practice, free NCERT Exemplar class 9 solutions maths Chapter 1 have been provided in downloadable PDF format. These exemplars contain solved problems, directly relevant to the exercises found in the NCERT textbook. Students can utilize these materials as valuable resources for revision, self-assessment, and exam preparation.

## NCERT Exemplar Class 9 Maths Chapter 1 FAQs

### Why should we download NCERT Exemplar Solutions for Class 9 Maths Chapter 1?

The presentation of each solution in the Chapter 1 of NCERT Exemplar Solutions for Class 9 Maths is described in a unique way by the Infinity Learn experts in Maths. The solutions are explained in easy language which improves grasping abilities among students. To score good marks, practising NCERT Exemplar Solutions for Class 9 Maths can help students to solve the paper. This chapter can be used as a model of reference by the students to improve their conceptual knowledge and understand the different ways used to solve the problems.

### Is INFINITY LEARN website providing answers to NCERT Exemplar Solutions for Class 9 Maths Chapter 1 in a detailed way?

Yes, Infinity Learn website provides answers to NCERT Exemplar Solutions for Class 9 Maths Chapter 1 in step by step manner. This allows the students to comprehend all the concepts in detail and also they can clear their doubts as well. Regular practising makes them score high in Maths Term I exams.

### Give an outline of concepts mentioned in NCERT Exemplar Solutions for Class 9 Maths Chapter 1.

NCERT Exemplar Solutions for Class 9 Maths Chapter 1 comprises 3 exercises. The concepts of this chapter are mentioned below. 1. Irrational Numbers 2. Real Numbers and their Decimal Expansions 3. Representing Real Numbers on the Number Line 4. Operations on Real Numbers 5. Laws of Exponents for Real Numbers

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