NCERT Solutions for Class 9 Maths

Q: Question 1. State whether the following statements are true or false. Give reasons for your answers. (i) Every natural number is a whole number. (ii) Every integer is a whole number. (iii) Every rational number is a whole number.

Answer: (i) True every natural is a whole number because natural number start from 1 and whole number start from 0, so every natural number is a whole number. (ii) True because an integer is a whole number ( not a fractional number ) that can be positive or zero. (iii) False a rational number is any number that can be expressed as the quotient of two integers.

Q: Question 2. Write three numbers whose decimal expansions are non-terminating non-recurring.

Answer: All irrational numbers have non-terminating and non-recurring decimal expression. So, $\sqrt{2}$, $\sqrt{3}$, and $\sqrt{5}$ will give such expressions. This is one of the various possible answers. It might have a different solution.

Q: Question 3. Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

Answer: No, for example $\sqrt{4}$ = 2 is a rational number. For example, $\sqrt{9}$ = 3, $\sqrt{16}$ = 4 is the rational numbers

Q: Question 4. Is zero a rational number? Can you write it in the form $\frac{p}{q}$, where p and q are integers and q $\neq$ =0? Write 1 if True and 0 if False

Answer: We know that a rational number is a number which can be written in the form of $\frac{p}{q}$, where q is not equal to zero. Thus, yes, zero is a rational number, as it can be written in the form of $\frac{p}{q}$. Since (zero) is an integer thus, zero can be written in the form of $\frac{p}{q}$ Example : $\frac{0}{1}$, $\frac{0}{2}$, $\frac{0}{3}$ etc. where 0 (zero) is an integer.

NCERT solutions for class 9 Maths is available to download for free from the links below. NCERT solutions are really helpful when it comes to a complicated subject like Mathematics. NCERT solutions for class 9 Maths will help you to understand and solve complex problems easily. It is time-saving and best study materials to follow for all the boards and especially CBSE boards.

NCERT solutions also help in cracking many competitive entrance exams like JEE Main, JEE Advanced, NEET, etc.

Class 9 Maths NCERT Solutions are available chapterwise on the app Toppr. Toppr app provides you a lot of free study materials, 1000+ hours of video lectures, mock tests, live doubt solving and more. You can signup or download Toppr app for Android or iOS.

Download NCERT solutions for all subjects of Class 9 here.

NCERT solutions for class 9 maths

NCERT Solutions for Class 9 Maths Chapterwise

Chapter 1 – Number Systems

Chapter 2 – Polynomials

Chapter 3 – Coordinate Geometry

Chapter 4 – Linear Equations in Two Variables

Chapter 5 – Introduction to Euclid’s Geometry

Chapter 6 – Lines and Angles

Chapter 7 – Triangles

Chapter 8 – Quadrilaterals

Chapter 9 – Area of Parallelograms and Triangles

Chapter 10 – Circles

Chapter 11 – Constructions

Chapter 12 – Heron’s Formula

Chapter 13 – Surface Areas and Volumes

Chapter 14 – Statistics

Chapter 15 – Probability

Class 9 Maths NCERT Solutions Chapterwise

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems

Rational numbers, Irrational numbers, Irrational numbers between two number are the topics covered under this chapter. We have solved more than 20 problems in this chapter. Download NCERT solutions for this chapter here.

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials

In this chapter, you will learn more about polynomials, degree of polynomials, and theorem related to it. We have solved more than 70 problems in this chapter. Download NCERT Solutions for this chapter here.

NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry

In this chapter, we have covered Distance formula, section formula, and more about the area of triangles and quadrilaterals. Download NCERT solutions for this chapter here.

NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables

We covered Linear equations in one variable in the previous Class, now it is time to solve two variables in equations. We have solved more than 30 problems in this chapter. Download NCERT Solutions for this chapter here.

NCERT Solutions for Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry

Euclid’s postulates, Axioms, Conjectures are the topics covered under this chapter. Download NCERT solutions for this chapter here.

NCERT Solutions for Class 9 Maths Chapter 6 Lines and Angles

In this chapter, you will learn about Geometry, Lines, and different types of angles. Geometry is one of the most important parts of Mathematics and NCERT solutions will help you understand it easily. Download NCERT Solutions for this chapter here.

NCERT Solutions for Class 9 Maths Chapter 7 Triangles

In this chapter, you will learn about the topics like properties of triangles, Pythagoras theorem, Basic proportionality theorem and more. This is one of the important chapters in CBSE Class 9 Maths. We have solved more than 50 solutions for this chapter. Download CBSE NCERT solutions for this chapter here.

NCERT Solutions for Class 9 Maths Chapter 8 Quadrilaterals

In this chapter, you will learn about Quadrilaterals and its properties and some theorems related to the quadrilateral. We have solved more than 50 solutions for this chapter. Download CBSE NCERT solutions for this chapter here.

NCERT Solutions for Class 9 Maths Chapter 9 Area of Parallelograms and Triangles

In this chapter, we will learn about calculating the area of triangles and parallelograms. Download NCERT solutions for this chapter here.

NCERT Solutions for Class 9 Maths Chapter 10 Circles

In this chapter, you will learn about the Arc of circle, tangents, cyclic quadrilateral and more. Download NCERT solutions for this chapter here.

NCERT Solutions for Class 9 Maths Chapter 11 Constructions

In this chapter, you will learn about the constructions of triangles, segments, tangent to a circle and more. Download NCERT solutions for this chapter here.

NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula

Heron’s formula will help in measuring the surface area of Triangles. We have solved more than 20 problems in this chapter. Download NCERT Solutions for this chapter here.

NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes

In this chapter, you will learn about the surface area and volumes of different shapes like Cuboid, cubes, cylinder, etc. This chapter will help you to understand how to measure the dimensions of different shapes. Download CBSE NCERT solutions for this chapter here.

NCERT Solutions for Class 9 Maths Chapter 14 Statistics

Graphs, Charts, Frequency Distribution, Mean-Median-Mode are the topics covered under this chapter. This chapter will also help you in understand some of the business mathematics concepts. Download NCERT Solutions for this chapter here.

NCERT Solutions for Class 9 Maths Chapter 15 Probability

Probability is a complicated concept and also one of the most important. Probability is a topic which will also help you in solving real-life problems, business mathematics, and also important for many competitive entrance exams. Download NCERT Solutions for this chapter here.

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Solved Questions For You:

Question 1. State whether the following statements are true or false. Give reasons for your answers.

(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.

Answer:

(i) True every natural is a whole number because natural number start from $1$ and whole number start from $0$ , so every natural number is a whole number.

(ii) True because an integer is a whole number ( not a fractional number ) that can be positive or zero.

(iii) False a rational number is any number that can be expressed as the quotient of two integers.

Question 2. Write three numbers whose decimal expansions are non-terminating non-recurring.

Answer: All irrational numbers have non-terminating and non-recurring decimal expression.

So, $\sqrt{2}$, $\sqrt{3}$, and $\sqrt{5}$ will give such expressions.

This is one of the various possible answers. It might have a different solution.

Question 3. Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

Answer: No,

for example $\sqrt{4}$ = 2 is a rational number.

For example, $\sqrt{9}$ = 3, $\sqrt{16}$ = 4 is the rational numbers

Question 4. Is zero a rational number? Can you write it in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q $\neq$ = 0 ?$

Write $1$ if True and $0$ if False

Answer:

We know that a rational number is a number which can be written in the form of $\frac{p}{q}$, where $q$ is not equal to zero.

Thus, yes, zero is a rational number, as it can be written in the form of $\frac{p}{q}$.

Since (zero) is an integer thus, zero can be written in the form of $\frac{p}{q}$

Example : $\frac{0}{1}$, $\frac{0}{2}$, $\frac{0}{3}$ etc. where

0

(zero) is an integer.

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