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**NCERT Solutions Class 9 Maths Chapter 1 Number Systems Exercise 1.5-** NCERT Solutions for Class 9 Maths exercise 1.5 deals with the concepts of the type of numbers into rational and irrational numbers and also the use of certain mathematical operations. Mathematically, numbers are labelled into many units, particularly rational numbers, irrational numbers, natural numbers, whole numbers, integers and real numbers. Real numbers, as defined in exercise 1.5 Class 9 Maths are the combination of rational and irrational numbers, which might have positive or negative attributes. A number that can be broken down into parts and addressed as p/q where p and q are integers and q≠0 are rational numbers. Irrational numbers are numbers that can't be stated as a fraction with a number in the numerator and denominator.

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NCERT solutions for Class 9 Maths Chapter 1 exercise 1.5 includes five questions where four are lengthy and the remaining 1 among them is the brief solution which is based on the category of determining the numbers into rational and irrational numbers by using certain mathematical operations and the illustration of given numbers on the number line. The concepts associated with the number lines and mathematical operations are nicely defined in this Class 9 Maths chapter 1 exercise 1.5. The following exercises are also present along with Class 9 Maths Chapter 1 exercise 1.5.

The 9th class maths exercise 1.5 answers are authored by subject experts in straightforward language, ensuring ease of understanding. Additionally, they are accessible in PDF format, allowing students to download and utilize them conveniently.

- Number System Exercise 1.1
- Number System Exercise 1.2
- Number System Exercise 1.3
- Number System Exercise 1.4
- Number System Exercise 1.6

** Q1 (i) ** Classify the following numbers as rational or irrational:

** Answer: **

Value of is 2.23606798....

Now,

Now,

Since the number is in non-terminating non-recurring. Therefore, it is an irrational number.

** Q1 (ii) ** Classify the following numbers as rational or irrational:

** Answer: **

Given number is

Now, it is clearly a rational number because we can represent it in the form of

** Q1 (iii) ** Classify the following numbers as rational or irrational:

** Answer: **

Given number is

As we can clearly see that it can be represented in form. Therefore, it is a rational number.

** Q1 (iv) ** Classify the following numbers as rational or irrational:

** Answer: **

Given number is

Now,

Clearly, as the decimal expansion of this expression is non-terminating and non-recurring. Therefore, it is an irrational number.

** Q1 (v) ** Classify the following numbers as rational or irrational:

** Answer: **

Given number is

We know that the value of

Now,

Now,

Clearly, as the decimal expansion of this expression is non-terminating and non-recurring. Therefore, it is an irrational number.

** Q2 (i) ** Simplify each of the following expressions:

** Answer: **

Given number is

Now, we will reduce it into

Therefore, answer is

** Q2 (ii) ** Simplify each of the following expressions:

** Answer: **

Given number is

Now, we will reduce it into

Therefore, answer is ** 6 **

** Q2 (iii) ** Simplify each of the following expressions:

** Answer: **

Given number is

Now, we will reduce it into

Therefore, the answer is

** Q2 (iv) ** Simplify each of the following expressions:

** Answer: **

Given number is

Now, we will reduce it into

Therefore, the answer is ** 3 ** .

** Answer: **

There is no contradiction.

When we measure a length with scale or any other instrument, we only obtain an approximate rational value. We never obtain an exact value.

For this reason, we cannot say that either c or d is irrational.

Therefore, the fraction is irrational. Hence, the value of is approximately equal to

Therefore, is irrational.

** Q4 ** Represent on the number line.

** Answer: **

Draw a line segment OB of 9.3 unit. Then, extend it to C so that BC = 1 unit. Find the mid-point D of OC and draw a semi-circle on OC while taking D as its centre and OD as the radius. Now, Draw a perpendicular to line OC passing through point B and intersecting the semi-circle at E. Now, Take B as the centre and BE as radius, draw an arc intersecting the number line at F. the length BF is units.

** Q5 (i) ** Rationalise the denominators of the following:

** Answer: **

Given number is

Now, on rationalisation, we will get

Therefore, the answer is

** Q5 (ii) ** Rationalise the denominators of the following:

** Answer: **

Given number is

Now, on rationalisation, we will get

Therefore, the answer is

** Q5 (iii) ** Rationalise the denominators of the following:

** Answer: **

Given number is

Now, on rationalisation, we will get

Therefore, the answer is

** Q5 (iv) ** Rationalise the denominators of the following:

** Answer: **

Given number is

Now, on rationalisation, we will get

Therefore, the answer is

The NCERT solutions for Class 9 Maths exercise 1.5 in particular defined the class of numbers into rational and irrational numbers via way of means of the usage of operations like commutative, associative, and distributive laws and additionally how they obey all of the laws and the illustration of given real number at the number line. Exercise 1.5 Class 9 Maths, includes some mathematical operations like commutative, associative, and distributive law. The commutative property states that When two numbers are added or multiplied together, the commutative law asserts that a change in their places has no effect on the outcome.

**Commutative law :**

A+B=B+A (Addition)

A×B=B×A (Multiplication)

The sum or product of three or more integers remains the same regardless of how the numbers are arranged, according to associative law.

**Associative law :**

(A+B)+C=A+(B+C) (Addition)

(AB)C=A(BC) ( Multiplication)

When a number is multiplied by the addition of two words, the distributive law dictates that each of the two numbers must be multiplied by the number.

**Distributive law :**

A(B+C)=AB+AC

**Also Read| **Number Systems Class 9 Notes

• NCERT solutions for Class 9 Maths exercise 1.5 able us to develop our basic concepts regarding numbers and their characteristics.

• By solving the NCERT solution for Class 9 Maths chapter 1 exercise 1.5 exercises, it develops a strong foundation of Mathematical knowledge and of course more confidence in tackling new topics in our higher classes.

• Exercise 1.5 Class 9 Maths, will help us in learning how to perform operations on real numbers and this may help us in higher classes.

**Application of Concepts**: This ex 1.5 class 9 often requires students to apply the concepts learned in the chapter to solve real-world problems.**Challenging Problems**: Some class 9 maths ex 1.5 questions may be more challenging, requiring students to think critically and use problem-solving skills.**Practice for Competitive Exams**: The questions in exercise 1.5 class 9 maths may serve as good practice for students preparing for competitive exams or Olympiads.**Enhances Problem-Solving Skills**: Solving class 9 ex 1.5 problems enhances students' problem-solving and analytical skills.**Step-by-Step Solutions**: Class 9 Maths Chapter 1 exercise 1.5 provides step-by-step solutions for Exercise 1.5 in the textbook or through supplementary materials, helping students understand the problem-solving process.**Self-assessment**: After solving the questions in this exercise, students can assess their understanding of the chapter's concepts.**Preparation for Board Exams**: 9th class maths exercise 1.5 answers are aligned with the CBSE board exam pattern, making it essential for board exam preparation.

Overall, Exercise 1.5 in Class 9 Maths serves as a crucial component of the curriculum, helping students practice and reinforce the mathematical concepts learned in the chapter.

**Also see-**

1. According to NCERT solutions for Class 9 Maths, 1 exercise 1.5 The associative property is applicable to ______

The associative property is applicable to Addition and Multiplication

Option (c) Addition and Multiplication

2. State true or false: The product of rational and irrational numbers is always an irrational number

Yes, the given statement is true. The product of a rational and an irrational number is always an irrational number.

3. Which property do the given statements hold? 2+3=3+2

2+3=3+2 holds the commutative property of addition.

4. Give one example for the commutative property of multiplication.

The example for the commutative property of multiplication is 5×2=2×5

5. Which of the two operations satisfy the condition of the associative property?

The two operations which satisfy the condition of the associative property are

Addition

Multiplication.

6. According to NCERT solutions for Class 9 Maths chapter 1 exercise 1.5, state the commutative property?

Commutative law states that when two numbers are added or multiplied together, a change in their locations has no effect on the outcome, according to NCERT solutions for Class 9 Maths chapter 1 exercise 1.5.

7. What is the total number of questions in the NCERT solutions for Class 9 Maths chapter 1 exercise 1.5 and What kind of questions are asked in NCERT solutions for Class 9 Maths chapter 1 exercise 1.5?

NCERT solutions for Class 9 Maths chapter 1 exercise 1.5 consists of 5 questions which are based on the classification of numbers into rational and irrational numbers by using certain operations and the representation of a given real number on the number line.

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