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NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

Edited By Komal Miglani | Updated on Jul 10, 2025 10:18 AM IST

Before we start investigating real numbers, it is important to first understand one of their close relatives - rational numbers. In a world full of numbers and uncertainty, rational numbers provide insight that everything can actually be divided logically and fairly. With rational numbers, it even begins to help to make sense of fractions, providing clarity where there was confusion. This is possible because rational numbers are numbers that can be written as pq, where p and q are integers, and q is not zero. Class 8 Maths NCERT Chapter 1, Rational Numbers, introduces students to rational numbers and their properties, including closure, associativity, commutativity, and distributivity. The main goal of these NCERT Solutions for class 8 of Rational Numbers is to provide students with solutions for the exercises in the textbook step-by-step so that they can always refer to the study material with the exercises when they are dealing with difficulties.

This Story also Contains
  1. Rational Numbers Class 8 Questions And Answers PDF Free Download
  2. Rational Numbers Class 8 NCERT Solutions (Exercise)
  3. Rational Numbers Class 8 Maths Chapter 1: Topics
  4. Rational Numbers Class 8 Solutions - Important Formulae
  5. NCERT Solutions for Class 8 Maths: Chapter Wise
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers

Rational numbers provide us with the understanding of sharing, measuring and balancing in the world of numbers. Rational numbers are everywhere and impact our lives daily, when sharing a bill, baking a cake, sharing a pizza, or solving an equation. In previous classes, students have already studied real numbers, whole numbers, natural numbers, and integers. So, these NCERT solutions for class 8 Maths on Rational Numbers Class 8 will complete the learning of the number system like a cherry on the cake. For quick access to your syllabus, notes, and PDFs, head over to the following link: NCERT.

Rational Numbers Class 8 Questions And Answers PDF Free Download

Students who wish to access the NCERT solutions for class 8, chapter 1, Rational Numbers, can click on the link below to download the entire solution in PDF.

Rational Numbers Class 8 NCERT Solutions (Exercise)

Try These Questions: Closure Property
Page Number: 4


Addition

Subtraction

Multiplication

Division

Rational Numbers

Yes

Yes

...

No

Integers

...

Yes

...

No

Whole Numbers

...

...

Yes

...

Natural Numbers

...

No

...

...

Answer:
It can be seen that rational numbers, integers, whole numbers, and natural numbers are not closed under division because Zero is included in these numbers. Any number divided by zero is not defined.


Addition

Subtraction

Multiplication

Division

Rational Numbers

Yes

Yes

Yes

No

Integers

Yes

Yes

Yes

No

Whole Numbers

Yes

No

Yes

No

Natural Numbers

Yes

No

Yes

Yes


Try These Questions: Commutative Property
Page Number: 6

Complete the following table:

Commutative for


Addition

Subtraction

Multiplication

Division

Rational Numbers

Yes

..

...

...

Integers

...

No

...

...

Whole Numbers

...

...

Yes

...

Natural Numbers

...

...

...

No

Answer:
In rational numbers, a ÷ b ≠ b ÷ a

also a-b ≠ b-a


Addition

Subtraction

Multiplication

Division

Rational Numbers

Yes

No

Yes

No

Integers

Yes

No

Yes

No

Whole Numbers

Yes

No

Yes

No

Natural Numbers

Yes

No

Yes

No


Try These Questions: Associative Property
Page Number: 9

Complete the following table:

Associative for


Addition

Subtraction

Multiplication

Division

Rational Numbers

...

...

...

No

Integers

...

...

Yes

...

Whole Numbers

Yes

...

...

...

Natural Numbers

...

No

...

...

Answer:
For associative in multiplication:- a × (b × c) = (a × b) × c


Addition

Subtraction

Multiplication

Division

Rational Numbers

Yes

No

Yes

No

Integers

Yes

No

Yes

No

Whole Numbers

Yes

No

Yes

No

Natural Numbers

Yes

No

Yes

No


Try These Questions: Distributivity
Page Number: 12

Find using distributivity:

Find using distributivity.
(i) {75×(312)}+{75×512}
(ii) {916×412}+{916×39}

Answer:
(i)
{75×(312)}+{75×512}
=75×(312+512)
=75×(3+512)
=75×16
=7×15×6
=730

(ii)
{916×412}+{916×39}
=916×(412+39)
=916×(1313)
=916×0
=0

NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers: Exercise: 1.1
Total Questions: 3
Page Number: 12

Question 1: Name the property under multiplication used in each of the following.

(i) 45×1=1×45=45
(ii) 1317×27=27×1317
(iii) 1929×2919=1

Answer:
(i) Multiplying any number by 1, we get the same number back.

i.e., a × 1 = 1 × a = a

Hence, 1 is the multiplicative identity for rational numbers.

(ii) Commutativity property states that a × b = b × a

(iii) Here Multiplicative Inverse Property is used.
Each number has an inverse (reciprocal), and the product of a number and its inverse is 1.
In this case, 1929 and 2919 are multiplicative inverses.

Question 2: Tell what property allows you to compute 13×(6×43) as (13×6)×43

Answer:
By the Associativity property for multiplication, we know that a × (b × c) = (a × b) × c.
Thus property used here is associativity.

Question 3: The product of two rational numbers is always a _______.

Answer:

Rational number. We know that if p and q are 2 rational numbers, then pq is also a rational number.

Rational Numbers Class 8 Maths Chapter 1: Topics

The topics discussed in the NCERT Solutions for class 8, chapter 1, Rational numbers, are:

  • Properties Of Rational Numbers

  • Representation Of Rational Numbers On The Number Line

  • Rational Numbers Between Rational Numbers

Rational Numbers Class 8 Solutions - Important Formulae

Here are some important formulas that will help students to solve problems related to rational numbers.

PropertyFormula
Additive Identityab+0=ab
Multiplicative Identityab×1=ab
Additive Inverseab+(ab)=0
Multiplicative Inverseab×ba=1
Closure (Addition)ab+cd is a rational number
Closure (Subtraction)abcd is a rational number
Closure (Multiplication)ab×cd is a rational number
Closure (Division)Not closed under division
Commutative (Addition)ab+cd=cd+ab
Commutative (Multiplication)ab×cd=cd×ab
Associative (Addition)(ab+cd)+ef=ab+(cd+ef)
Associative (Multiplication)(ab×cd)×ef=ab×(cd×ef)
Distributive Propertyab×(cd+ef)=(ab×cd)+(ab×ef)

NCERT Solutions for Class 8 Maths: Chapter Wise

For students' preparation, Careers360 has gathered all Class 8 Maths NCERT solutions here for quick and convenient access.

NCERT Solutions for Class 8: Subject-Wise

Careers360 also provides well-structured and well-explained solutions for other subjects. The following links can be used for those purposes.

NCERT Books and NCERT Syllabus

Students can use the following links to download the latest version of the CBSE syllabus and some other reference books for class 8.

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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