NCERT Solutions for Class 7 Mathematics Chapter 9: Rational Numbers

Content Curator

NCERT Solutions for Class 7 Mathematics Chapter 9 Rational Numbers are provided in this article. A rational number is a number that can be expressed as a ratio of p/q, where p and q are integers, and q does not equal to zero. The numerator and the denominator of a rational number will be integers. Some of the important topics in Rational Numbers chapter include:

Rationalize the Denominator
Number Systems
Operations on Rational Numbers
Relation Between HCF and LCM
Decimal Expansion of Rational Numbers
Irrational Numbers

Download PDF: NCERT Solutions for Class 7 Mathematics Chapter 9 pdf

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers is given below.

Class 7 Maths Chapter 9 Rational Numbers – Important Topics

Rational Number: A rational number is a number which is represented as a ratio of two numbers in the form p/q where 'q' is not equal to zero and both 'p' and 'q' are integers.

Number 8 can be written as fraction 8/1, it will be a rational number.
3/4 can be written as a fraction since it is a rational number.
We can write the decimal 1.5 as the ratio of 3/2. Therefore, it is also a rational number
O.333...can be written as 1/3. So it is a rational number
Recurring decimals like 0.262626..., all finite decimals andl integers are also rational numbers.

Example: If A had 5/8 litres of milk and gave 3/5 literes of milk to B. How much is left with A?

Ans. A gave 3/5 litres of milk from 5/8 litres.

Thus,

5/8 – 3/5

= (25 – 24) / 40

= 1/40 litres of milk is left with A.

NCERT Solutions for Class 7 Maths Chapter 9 Exercises

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Exercises are given below.

Read More:

Reciprocal and Division of Fractions	Properties of Rational Numbers	Reciprocals
Additive Identity and Multiplicative Identity	Distributive Properties	Distributive Properties Formula

Class 7 Maths Study Guides:

NCERT Solutions for Class 7 Maths	Number System	Geometry
Arithmetics	Basic Maths	Maths Formulas

CBSE X Related Questions

1.
Given that $\sin \theta + \cos \theta = x$, prove that $\sin^4 \theta + \cos^4 \theta = \dfrac{2 - (x^2 - 1)^2}{2}$.
View Solution
2.
Prove that: \[ \frac{\cos \theta - 2 \cos^3 \theta}{\sin \theta - 2 \sin^3 \theta} + \cot \theta = 0 \]
View Solution
3.
Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
(i) $pqr + 1$ is a composite number
(ii) $pqr + 1$ is a prime number
View Solution
4.
In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$.
View Solution
5.
Find the mean and mode of the following data:
Class 15--20 20--25 25--30 30--35 35--40 40--45
Frequency 12 10 15 11 7 5
View Solution
6.
The given figure shows a circle with centre O and radius 4 cm circumscribed by $\triangle ABC$. BC touches the circle at D such that BD = 6 cm, DC = 10 cm. Find the length of AE.
View Solution

View All

Mathematics Preparation Guides

Area of a Triangle: Formula, Types & Examples

Isosceles Triangle Theorems: Proof and Sample Questions

How to Calculate Percentage: Formula, Basic Tricks, Solved Examples

Difference Between Area and Perimeter: Definitions & Formulas

Area of Square Using Diagonal: Formula, Relation & Derivation

Additive Inverse: Formula, Properties, Fraction & Complex Numbers

BODMAS Rule: Definition, Rules and Sample Questions

Isosceles Right Triangle: Formulas, Pythagoras Theorem and Area

Unitary Method: Steps, Types of Unitary Method, Solved Examples

Triangle Theorems: Properties, Types & Similarity Theorems

Percentage: Formula, Conversions and Examples

Area of Isosceles Triangle: Formula, Properties & Examples

Area and Perimeter: Definition, Formulas & Examples

Commutative Property: Formula, Properties, Sample Questions

Perimeter of a Trapezoid Formula: Perimeter, Quadrilateral, Polygons

Interest Formula: Simple and Compound Interest, Differences

Percentage Formula: How to Calculate Percentage?

Difference Between In Maths: Comparison Articles

Percentage Change, Percent Decrease Formula, Sample Questions

Percentage Change Formula: Solved Examples

Mathematics NCERT Solutions

Difference Between Cube and Cuboid: Explanation and Examples

Triangle Inequality Theorem: Mechanism and Proof

NCERT Solutions for Class 7 Mathematics Chapter 1: Integers

NCERT Solutions for Class 7 Mathematics Chapter 10: Practical Geometry

NCERT Solutions for Class 7 Mathematics Chapter 14: Symmetry

NCERT Solutions for Class 7 Mathematics Chapter 5: Lines and Angles

NCERT Solutions For Class 7 Science Chapter 15 : Visualizing Solid Shapes

NCERT Solutions For Class 7 Mathematics Chapter 4: Simple Equations

NCERT Solutions for Class 7 Mathematics Chapter 8: Comparing Quantities

NCERT Solutions for Class 7 Mathematics Chapter 3: Data Handling

NCERT Solutions for Class 7 Mathematics Chapter 9: Rational Numbers

Download PDF: NCERT Solutions for Class 7 Mathematics Chapter 9 pdf

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers

Class 7 Maths Chapter 9 Rational Numbers – Important Topics

NCERT Solutions for Class 7 Maths Chapter 9 Exercises

CBSE X Related Questions

1.
Given that $\sin \theta + \cos \theta = x$, prove that $\sin^4 \theta + \cos^4 \theta = \dfrac{2 - (x^2 - 1)^2}{2}$.

2.
Prove that: \[ \frac{\cos \theta - 2 \cos^3 \theta}{\sin \theta - 2 \sin^3 \theta} + \cot \theta = 0 \]

3.
Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
(i) $pqr + 1$ is a composite number
(ii) $pqr + 1$ is a prime number

4.
In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$.

5.
Find the mean and mode of the following data:
Class 15--20 20--25 25--30 30--35 35--40 40--45
Frequency 12 10 15 11 7 5

6.
The given figure shows a circle with centre O and radius 4 cm circumscribed by \(\triangle ABC\). BC touches the circle at D such that BD = 6 cm, DC = 10 cm. Find the length of AE.

Comments

SUBSCRIBE TO OUR NEWS LETTER

Class	15--20	20--25	25--30	30--35	35--40	40--45
Frequency	12	10	15	11	7	5

NCERT Solutions for Class 7 Mathematics Chapter 9: Rational Numbers

​Download PDF: NCERT Solutions for Class 7 Mathematics Chapter 9 pdf

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers

Class 7 Maths Chapter 9 Rational Numbers – Important Topics

NCERT Solutions for Class 7 Maths Chapter 9 Exercises

CBSE X Related Questions

1.Given that $\sin \theta + \cos \theta = x$, prove that $\sin^4 \theta + \cos^4 \theta = \dfrac{2 - (x^2 - 1)^2}{2}$.

2.Prove that: \[ \frac{\cos \theta - 2 \cos^3 \theta}{\sin \theta - 2 \sin^3 \theta} + \cot \theta = 0 \]

3.Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that (i) $pqr + 1$ is a composite number (ii) $pqr + 1$ is a prime number

4.In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$.

5.Find the mean and mode of the following data:Class15--2020--2525--3030--3535--4040--45Frequency1210151175

6.The given figure shows a circle with centre O and radius 4 cm circumscribed by \(\triangle ABC\). BC touches the circle at D such that BD = 6 cm, DC = 10 cm. Find the length of AE.

Comments

SUBSCRIBE TO OUR NEWS LETTER

Download PDF: NCERT Solutions for Class 7 Mathematics Chapter 9 pdf

1.
Given that $\sin \theta + \cos \theta = x$, prove that $\sin^4 \theta + \cos^4 \theta = \dfrac{2 - (x^2 - 1)^2}{2}$.

2.
Prove that: \[ \frac{\cos \theta - 2 \cos^3 \theta}{\sin \theta - 2 \sin^3 \theta} + \cot \theta = 0 \]

3.
Let $p$, $q$ and $r$ be three distinct prime numbers. Check whether $pqr + q$ is a composite number or not. Further, give an example for three distinct primes $p$, $q$, $r$ such that
(i) $pqr + 1$ is a composite number
(ii) $pqr + 1$ is a prime number

4.
In the adjoining figure, TP and TQ are tangents drawn to a circle with centre O. If $\angle OPQ = 15^\circ$ and $\angle PTQ = \theta$, then find the value of $\sin 2\theta$.

5.
Find the mean and mode of the following data:
Class 15--20 20--25 25--30 30--35 35--40 40--45
Frequency 12 10 15 11 7 5

6.
The given figure shows a circle with centre O and radius 4 cm circumscribed by \(\triangle ABC\). BC touches the circle at D such that BD = 6 cm, DC = 10 cm. Find the length of AE.