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NCERT Solutions Class 7 Maths 2024 – Download PDF

NCERT Solutions Class 7 Maths: NCERT solutions are a great way to learn the concepts and how to solve problems correctly. Maths is one of the main subjects in the Class 7 curriculum and forms the fundamentals for concepts that will be needed in the higher classes. Referring to them can help them score good marks and prepare for the exam efficiently.

Embibe provides NCERT solutions for Class 7 Maths for all intext and exercise questions. The solutions have a step-by-step approach to solving problems with clear explanations. Apart from this, Embibe provides over 1000+ practice questions for all 15 chapters along with chapter-wise mock tests and full tests. Continue reading to learn more about the NCERT solutions for Class 7 Maths and ace the exam.

NCERT Solutions Class 7 Maths

Class 7 Maths deals with topics like integers, data handling, triangles and properties, and many more. These concepts are all needed to understand complex topics in the later classes. To ace the examination students should learn the Class 7 Maths concepts on Embibe through 3D videos and Embibe explainers.

Additionally, they can also practice questions for better comprehension. Referring to NCERT solutions can help them grasp the concepts firmly and how to solve the problems systematically so that they can tackle any question that comes up in the exam. Before going to the solutions, students can find the chapters for Class 7 Maths in the following table.

NCERT Solutions for Class 7 Maths: Points to Remember

Besides learning and practicing, students can also take the Class 7 Maths mock tests on Embibe to assess their preparation. And while revising they can refer to some important points to quickly recall the concepts. Below are some of the important points that students must remember about the NCERT Solutions for Class 7 Maths:

• On an integer number line, all numbers to the right of 0 are positive integers and all numbers to the left of 0 are negative integers.
• All the properties applicable to whole numbers are applicable to integers in addition, the subtraction operation has the closure property.
• A fraction whose numerator is less than the denominator is called a proper fraction.
• Fractions having the same denominators are called like fractions. Otherwise, they are called unlike fractions.
• Mode is another form of central tendency or representative value. The mode of a set of observations is the observation that occurs most often.
• In an equation, we can move a term from one side to the other side with the opposite sign. This process is known as transposition.
•  The distance between two parallel lines is the same everywhere and is equal to the perpendicular distance between them.
• The three line segments forming a triangle are called the sides of the triangle.
• Two triangles are congruent if the three sides and the three angles of one triangle are respectively equal to the corresponding parts of the other.
• We can also use the idea of ‘equal corresponding angles’ to do the construction.
• The number π is not a rational number.

NCERT Solutions for Class 7 Maths: All Chapters

Referring to NCERT solutions is really helpful to level up for exam preparation. To help students get easy access to NCERT solutions, we have provided the solutions for all chapters of Class 7 Maths. Students can click on the links below and start practicing right away.

• 1st Chapter: Integers
• 2nd Chapter: Fractions and Decimals
• 3rd Chapter: Data Handling
• 4th Chapter: Simple Equations
• 5th Chapter: Lines and Angles
• 6th Chapter: The Triangle and Its Properties
• 7th Chapter: Congruence of Triangles
• 8th Chapter: Comparing Quantities
• 9th Chapter: Rational Numbers
• 10th Chapter: Practical Geometry
• 11th Chapter: Perimeter and Area
• 12th Chapter: Algebraic Expression
• 13th Chapter: Exponents and Powers
• 14th Chapter: Symmetry
• 15th Chapter: Visualizing Solid Shapes

FAQs on NCERT Solutions for Class 7 Maths 2023-24

Some of the frequently asked questions on the NCERT Solutions for Class 7 Maths are as follows:

Ans: Students can find the NCERT solutions for Class 7 Maths on Embibe.

Ans: Embibe provides numerous practice questions for Class 7 Maths.

Ans: There are 15 chapters in NCERT solutions for Class 7 Maths.

Ans: Students can take the Class 7 Maths mock tests on Embibe.

Ans: Referring to the NCERT solutions for Class 7 Maths helps students grasp the concepts and learn the correct approach to solving problems.

We hope this detailed article on NCERT Solutions for Class 7 Maths helps you. For more such articles, stay tuned to Embibe .

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NCERT Solutions for Class 6, 7, 8, 9, 10, 11 and 12

NCERT Solutions for Class 7 Maths

If you are looking for NCERT Solutions for Class 7 Maths, you have come to the right place. Experienced LearnCBSE.in Teachers has created detailed CBSE 7th class maths textbook solutions. We provide that are precise to the point and absolutely error free. NCERT class 7 maths solutions includes all the questions provided as per new revised syllabus in NCERT Class 7 Maths textbook. NCERT maths book class 7 solutions pdf can be downloaded in One click without LOGIN. You can also practice  Extra Questions for Class 7 Maths  on LearnCBSE.in

Chapter wise detailed NCERT Solutions for Class 7 Maths are given below.

• Chapter 1 Integers
• Chapter 2 Fractions and Decimals
• Chapter 3 Data Handling
• Chapter 4 Simple Equations
• Chapter 5 Lines and Angles
• Chapter 6 The Triangles and its Properties
• Chapter 7 Congruence of Triangles
• Chapter 8 Comparing Quantities
• Chapter 9 Rational Numbers
• Chapter 10 Practical Geometry
• Chapter 11 Perimeter and Area
• Chapter 12 Algebraic Expressions
• Chapter 13 Exponents and Powers
• Chapter 14 Symmetry
• Chapter 15 Visualising Solid Shapes

You can also download the free NCERT Solutions for Class 7 Maths All Chapters PDF or save the solution images and take the print out to keep it handy for your exam preparation.

NCERT Solutions for Class 7 Maths Chapter 1 Integers

• Class 7 Maths Integers Exercise 1.1 
• Class 7 Maths Integers Exercise 1.2
• Class 7 Maths Integers Exercise 1.3
• Class 7 Maths Integers Exercise 1.4
• Integers Class 7 Extra Questions

NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals

• Class 7 Maths Fractions and Decimals Exercise 2.1 
• Class 7 Maths Fractions and Decimals Exercise 2.2
• Class 7 Maths Fractions and Decimals Exercise 2.3
• Class 7 Maths Fractions and Decimals Exercise 2.4
• Class 7 Maths Fractions and Decimals Exercise 2.5
• Class 7 Maths Fractions and Decimals Exercise 2.6
• Class 7 Maths Fractions and Decimals Exercise 2.7
• Fractions and Decimals Class 7 Extra Questions

NCERT Solutions for Class 7 Maths Chapter 3 Data Handling

• Class 7 Maths Data Handling Exercise 3.1 
• Class 7 Maths Data Handling Exercise 3.2
• Class 7 Maths Data Handling Exercise 3.3
• Class 7 Maths Data Handling Exercise 3.4
• Data Handling Class 7 Extra Questions

NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations

• Class 7 Maths Simple Equations Exercise 4.1 
• Class 7 Maths Simple Equations Exercise 4.2
• Class 7 Maths Simple Equations Exercise 4.3
• Class 7 Maths Simple Equations Exercise 4.4
• Simple Equations Class 7 Extra Questions

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles

• Class 7 Maths Lines and Angles Exercise 5.1
• Class 7 Maths Lines and Angles Exercise 5.2
• Lines and Angles Class 7 Extra Questions

NCERT Solutions for Class 7 Maths Chapter 6 The Triangles and its Properties

• Class 7 Maths The Triangle and Its Properties Exercise 6.1
• Class 7 Maths The Triangle and Its Properties Exercise 6.2
• Class 7 Maths The Triangle and Its Properties Exercise 6.3
• Class 7 Maths The Triangle and Its Properties Exercise 6.4
• Class 7 Maths The Triangle and Its Properties Exercise 6.5
• The Triangles and its Properties Class 7 Extra Questions

NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles

• Class 7 Maths Congruence of Triangles Exercise 7.1
• Class 7 Maths Congruence of Triangles Exercise 7.2
• Congruence of Triangles Class 7 Extra Questions

NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities

• Class 7 Maths Comparing Quantities Exercise 8.1 
• Class 7 Maths Comparing Quantities Exercise 8.2
• Class 7 Maths Comparing Quantities Exercise 8.3
• Comparing Quantities Class 7 Extra Questions

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers

• Class 7 Maths Rational Numbers Exercise 9.1 
• Class 7 Maths Rational Numbers Exercise 9.2
• Rational Numbers Class 7 Extra Questions

NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry

• Class 7 Maths Practical Geometry Exercise 10.1
• Class 7 Maths Practical Geometry Exercise 10.2
• Class 7 Maths Practical Geometry Exercise 10.3
• Class 7 Maths Practical Geometry Exercise 10.4
• Class 7 Maths Practical Geometry Exercise 10.5
• Practical Geometry Class 7 Extra Questions

NCERT Solutions for Class 7 Maths Chapter 11 Perimeter and Area

• Class 7 Maths Perimeter and Area Exercise 11.1 
• Class 7 Maths Perimeter and Area Exercise 11.2
• Class 7 Maths Perimeter and Area Exercise 11.3
• Class 7 Maths Perimeter and Area Exercise 11.4
• Perimeter and Area Class 7 Extra Questions

NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions

• Class 7 Maths Algebraic Expressions Exercise 12.1 
• Class 7 Maths Algebraic Expressions Exercise 12.2
• Class 7 Maths Algebraic Expressions Exercise 12.3
• Class 7 Maths Algebraic Expressions Exercise 12.4
• Algebraic Expressions Class 7 Extra Questions

NCERT Solutions for Class 7 Maths Chapter 13 Exponents and Powers

• Class 7 Maths Exponents and Powers Exercise 13.1 
• Class 7 Maths Exponents and Powers Exercise 13.2
• Class 7 Maths Exponents and Powers Exercise 13.3
• Exponents and Powers Class 7 Extra Questions

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

• Class 7 Maths Symmetry Exercise 14.1 
• Class 7 Maths Symmetry Exercise 14.2
• Class 7 Maths Symmetry Exercise 14.3
• Symmetry Class 7 Extra Questions

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes

• Class 7 Maths Visualising Solid Shapes Exercise 15.1 
• Class 7 Maths Visualising Solid Shapes Exercise 15.2
• Class 7 Maths Visualising Solid Shapes Exercise 15.3
• Class 7 Maths Visualising Solid Shapes Exercise 15.4
• Visualising Solid Shapes Class 7 Extra Questions

NCERT Solutions for Class 7 Maths (Download PDF) Maths NCERT Solutions Maths Formulas for Class 7

Key Features Class 7 Maths NCERT Solutions:

• Class 7 Maths NCERT Solutions were prepared by subject experts.
• Step by step solutions to understand problems better.
• Detailed Explanation to solve problems and formulas are mentioned in between steps to learn effectively.
• Exercise wise Class 7 Maths solutions also given to access easily.
• You can download NCERT Solutions for Class 7 Maths PDF or save the solution images and take the print out to keep it handy for your exam preparation.

We make it a point to assist students in every possible manner we can, and that includes providing solutions for every subject. NCERT textbooks have been reputed to be the best textbooks for school education, and we make the solutions competent for the books.

Mathematics comes across a rather dreadful subject for most students in school, and we believe that a little practice can sort that problem, Therefore, our solutions focus on building the concepts based on the fundamentals, and also exploring alternative methods to solve a particular problem.

Browse all Class 7 Maths NCERT Solutions from your tablet, desktop or mobile and score more marks in your final exams. You can also go through the RD Sharma Class 7 Solutions and RS Aggarwal Class 7 Solutions which will help you in extra practice and exams.

Here is the list of Main Topics from Class 7 Maths NCERT Text Book:

Class 7 Maths Chapter 1 Integers

After an introduction to whole numbers in class 6, this chapter deals with integers, both positive and negative, to give the students a feel of the real numbers. This chapter gives a new perspective to students, in terms of properties and importance of integers. The exercises are made to ensure that the students grasp the whole concept thoroughly.

• 1.1 Introduction
• 1.3 Properties Of Addition And Subtraction Of Integers
• 1.4 Multiplication Of Integers
• 1.5 Properties Of Multiplication Of Integers
• 1.6 Division Of Integers
• 1.7 Properties Of Division Of Integers

Class 7 Maths Chapter 2 Fractions and Decimals

This is not exactly a new concept, rather, a further exploration of the old concepts. The chapter deals with the properties of fractions and decimals, and the operations on the same. They also deal with the portrayal of fractions and decimals on the number line, and their expansions and subtraction.

• 2.1 Introduction
• 2.2 How Well Have You Learnt About Fractions?
• 2.3 Multiplication Of Fractions
• 2.4 Division Of Fractions
• 2.5 How Well Have You Learnt About Decimal Numbers
• 2.6 Multiplication Of Decimal Numbers
• 2.7 Division Of Decimal Numbers

Class 7 Maths Chapter 3 Data Handling

This chapter can be considered as the first step towards statistics, as it deals with data accumulation, the data interpretation, and the plotting, keeping up with real life examples. The chapters also teach how to make a few deductions from the accumulated data. The exercises are kept very close to real life examples, and thus, practicing the same gives a better feel of the same.

• 3.1 Introduction
• 3.2 Collecting Data
• 3.3 Organisation Of Data
• 3.4 Representative Values
• 3.5 Arithmetic Mean
• 3.8 Use Of Bar Graphs With A Different Purpose
• 3.9 Chance And Probability

Class 7 Maths Chapter 4 Simple Equations

As the name suggests, this chapter deals with the formulation and applications of simple equations. From setting up simple equations to solving them, this chapter explores the theory of equations thoroughly. The problems have been extensively discussed in the solutions.

• 4.1 A Mind-Reading Game!
• 4.2 Setting Up Of An Equation.
• 4.3 Review Of What We Know.
• 4.4 What Equation Is?
• 4.5 More Equations.
• 4.6 From Solution To Equation.
• 4.7 Applications Of Simple Equations To Practical Situations.

Class 7 Maths Chapter 5 Lines and Angles

The first chapter of geometry in Class 7, lines and angles starts with the fundamental definitions of line and angle. The chapter will cruise through the concepts of parallel lines, and the associated angles like the alternate interior angles, corresponding angles, vertically opposite angles. This fairly easy chapter is further made interesting with the help of exercises, and the solutions justify the same effectively.

• 5.1 Introduction.
• 5.2 Related Angles.
• 5.3 Pairs Of Lines.
• 5.4 Checking For Parallel Lines.

Class 7 Maths Chapter 6 The triangle and its properties

The second chapter of geometry deals with triangles and their properties. This chapter talks about the types of triangles, the angle sum property, the medians and altitudes, and the Pythagoras theorem. The students will get a feel of what triangles are in general, and the specific applications of the Pythagoras theorem in this chapter.

• 6.1 Introduction.
• 6.2 Medians Of A Triangle.
• 6.3 Altitudes Of A Triangle.
• 6.4 Exterior Angle Of A Triangle And Its Property.
• 6.5 Angle Sum Property Of A Triangle.
• 6.6 Two Special Triangles: Equilateral And Isosceles.
• 6.7 Sum Of The Lengths Of Two Sides Of A Triangle.
• 6.8 Right-Angled Triangles And Pythagoras Property.

Class 7 Maths Chapter 7 Congruence of Triangles

After the general introduction of triangles in Chapter 6, the seventh chapter deals with the specific property of congruence of triangles. The chapter covers all the congruence criteria, and deal with different kinds of problems. The solutions discuss the congruence criteria extensively, using alternative approach wherever possible.

• 7.1 Introduction.
• 7.2 Congruence Of Plane Figures.
• 7.3 Congruence Among Line Segments.
• 7.4 Congruence Of Angles.
• 7.5 Congruence Of Triangles.
• 7.6 Criteria For Congruence Of Triangles.
• 7.7 Congruence Among Right-Angled Triangles.

Class 7 Maths Chapter 8 Comparing Quantities

This chapter can be safely assumed to be one of the most application oriented chapters in the whole Class 7 Mathematics syllabus. As the name suggests, this chapter gives the tool to measure and compare quantities. The tools are primarily percentage, ratios, profit and loss, and interest. The chapter comes in handy in all folds of life, as the calculations learnt here are the ones used in the real world the most.

• 8.1 Introduction.
• 8.2 Equivalent Ratios.
• 8.3 Percentage – Another Way Of Comparing Quantities.
• 8.4 Use Of Percentages.
• 8.5 Prices Related To An Item Or Buying And Selling.
• 8.6 Charge Given On Borrowed Money Or Simple Interest.

Class 7 Maths Chapter 9 Rational Numbers

After discussing integers extensively in the first chapter, this chapter comes back to the numbers, namely rational numbers. The chapter deals with the definitions and the properties of rational numbers.

• 9.1 Introduction
• 9.2 Need For Rational Numbers.
• 9.3 What Are Rational Numbers?
• 9.4 Positive And Negative Rational Numbers.
• 9.5 Rational Numbers On A Number Line.
• 9.6 Rational Numbers In Standard Form.
• 9.7 Comparison Of Rational Numbers.
• 9.8 Rational Numbers Between Two Rational Number.
• 9.9 Operations On Rational Numbers.

Class 7 Maths Chapter 10 Practical Geometry

This chapter deals with the portrayal of geometry on paper, in terms of construction of lines and angles. This is a fairly simpler chapter, that only requires a set procedure to be followed while going through constructions.

• 10.1 Introduction
• 10.2 Construction Of A Line Parallel To A Given Line, Through A Point Not On The Line.
• 10.3 Construction Of Triangles.
• 10.4 Constructing A Triangle When The Lengths Of Its Three Sides Are Known (SSS Criterion)
• 10.5 Constructing A Triangle When The Lengths Of Two Sides And The Measure Of The Angle Between Them Are Known. (SAS Criterion)
• 10.6 Constructing A Triangle When The Measures Of Two Of Its Angles And The Length Of The Side Included Between Them Is Given. (ASA Criterion)
• 10.7 Constructing A Right-Angled Triangle When The Length Of One Leg And Its Hypotenuse Are Given (RHS Criterion).

Class 7 Maths Chapter 11 Perimeter and Area

This chapter brings in the mensuration part of the syllabus. It deals with the areas and perimeters of all the important shapes in Mathematics. The chapter is very simple, without the introduction of any complex shapes.

• 11.1 Introduction.
• 11.2 Squares And Rectangles.
• 11.3 Area Of A Parallelogram.
• 11.4 Area Of A Triangle.
• 11.5 Circles.
• 11.6 Conversion Of Units.
• 11.7 Applications.

Class 7 Maths Chapter 12 Algebraic Equations

This chapter deals with converting simple mathematical statements into algebraic equations and using them to solve certain problems, using the principles of algebra. The mathematical statements are closely related to some of the real life examples, where the algebra can actually be used. The exercises make it double the fun.

• 12.1 Introduction.
• 12.2 How Are Expressions Formed?
• 12.3 Terms Of An Expression.
• 12.4 Like And Unlike Terms.
• 12.5 Monomials, Binomials, Trinomials And Polynomials.
• 12.6 Addition And Subtraction Of Algebraic Expressions.
• 12.7 Finding The Value Of An Expression.
• 12.8 Using Algebraic Expressions – Formulas And Rules.

Class 7 Maths Chapter 13 Exponents and Powers

This chapter deals with the introduction to exponents, the rules of multiplication and division of exponents, the power of a power, decimal system, and the expression of very large numbers into the Standard Form, or the Scientific Notation.

• 13.1 Introduction.
• 13.2 Exponents.
• 13.3 Laws Of Exponents.
• 13.4 Miscellaneous Examples Using The Laws Of Exponents.
• 13.5 Decimal Number System.
• 13.6 Expressing Large Numbers In The Standard Form.

Class 7 Maths Chapter 14 Symmetry

This chapter gives a perspective of symmetrical shapes to the students. Symmetry is exploited extensively by craftsmen and designers to plan out intricate design patterns. This chapter on symmetry is to give the students the general idea of symmetry in the world.

• 14.1 Introduction: Symmetry
• 14.2 Lines Of Symmetry For Regular Polygons.
• 14.3 Rotational Symmetry.
• 14.4 Line Symmetry And Rotational Symmetry.

Class 7 Maths Chapter 15 Visualising Solid Shapes

This chapter deals with the visuals of geometry, by explaining the various geometrical shapes that are incorporated in designing the everyday objects around us. This chapter deals with both plane figures as well as solid shapes.

• 15.1 Introduction: Plane Figures And Solid Shapes.
• 15.2 Faces, Edges, and Vertices.
• 15.3 Nets For Building 3-D Shapes.
• 15.4 Drawing Solids On A Flat Surface.
• 15.5 Viewing Different Sections Of A Solid.

FAQs on NCERT Solutions for Class 7 Maths

1.  How can I score good marks in the Maths in Class 7?

Go through the Concepts thoroughly and prepare as per the topics by using the NCERT Solutions. Make sure you develop a proper preparation strategy to clear the Class 7 Exam with ease.

2. Which is the best reference book for Class 7 Maths?

For basics, NCERT Textbooks prescribed by the CBSE Board are more than enough to score better grades in the Class 7 Maths Exam.

3.  Why are NCERT Solutions for Class 7 Maths important?

Class 7 Maths NCERT Solutions are prepared by experts and they give you step by step solutions to understand the problems better. They can be quite handy during your preparation.

4. How to download NCERT Solutions for Class 7 free?

Aspirants can download the NCERT Solutions for Class 7 free of cost from our site. Make use of them as a reference and aid your preparation.

5. What are the Chapters contained in the NCERT Solutions for Class 7 Maths?

You can go through the Chapter List for the NCERT Class 7 Maths Solutions by referring to our page. Refer to the topics under each chapter and plan your preparation accordingly.

6. Where can I get NCERT Solutions for Class 7th Maths?

You can get NCERT Solutions for Class 7th Maths by referring to our page. Access the direct links to view or download and use them as a reference during your preparation.

We hope you will have great learning experience while using the solutions. You can download the solutions by clicking on the links above in the description.

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NCERT Books

NCERT Books for Class 7 Maths PDF Download

NCERT Books Class 7 Maths : The National Council of Educational Research and Training (NCERT) publishes Maths textbooks for Class 7. The NCERT Class 7th Maths textbooks are well known for it’s updated and thoroughly revised syllabus. The NCERT Maths Books are based on the latest exam pattern and CBSE syllabus.

NCERT keeps on updating the Maths books with the help of the latest question papers of each year. The Class 7 Maths books of NCERT are very well known for its presentation. The use of NCERT Books Class 7 Maths is not only suitable for studying the regular syllabus of various boards but it can also be useful for the candidates appearing for various competitive exams, Engineering Entrance Exams, and Olympiads.

NCERT Class 7 Maths Books in English PDF Download

NCERT Class 7 Maths Books are provided in PDF form so that students can access it at any time anywhere. Class 7 NCERT Maths Books are created by the best professors who are experts in Maths and have good knowledge in the subject.

NCERT Books for Class 7 Maths – English Medium

• Chapter 1:  Integers

NCERT Solutions for class 7 Maths

• Chapter 2:  Fractions and Decimals
• Chapter 3:  Data Handling
• Chapter 4:  Simple Equations
• Chapter 5:  Lines and Angles
• Chapter 6:  The Triangles and Its Properties
• Chapter 7:  Congruence of Triangles
• Chapter 8:  Comparing Quantities
• Chapter 9:  Rational Numbers
• Chapter 10:  Practical Geometry
• Chapter 11:  Perimeter and Area
• Chapter 12:  Algebraic Expressions
• Chapter 13:  Exponents and Powers
• Chapter 14:  Symmetry
• Chapter 15:  Visualising Solid Shapes

NCERT Books for Class 7 Maths – Hindi Medium

• अध्याय 1:  पूर्णांक
• अध्याय 2:  भिन्न एवं दशमलव
• अध्याय 3:  आँकड़ो का प्रबंधन
• अध्याय 4:  सरल समीकरण
• अध्याय 5:  रेखा एवं कोण
• अध्याय 6:  त्रिभुज और उसके गुण
• अध्याय 7:  त्रिभुजों की सर्वांगसमता
• अध्याय 8:  राशियों की तुलना
• अध्याय 9:  परिमेय संख्याएँ
• अध्याय 10:  प्रायोगिक ज्यामिती
• अध्याय 11:  परिमाप और क्षेत्रफल
• अध्याय 12:  बीजीय व्यंजक
• अध्याय 13:  घातांक और घात
• अध्याय 14:  सममिति
• अध्याय 15:  ठोस आकारों का चित्रण

The NCERT syllabus mainly focuses on this book to make it student-friendly to make it useful for both the students and the competitive exam aspirants. The book covers a detailed Maths based on the syllabuses of various boards. NCERT Maths Books for Class 7 is perfectly compatible with almost every Indian education state and central boards.

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NCERT Solutions for Class 7 Maths Chapter 1 Integers

NCERT Solutions for Class 7 Maths Chapter 1 Integers are available here. When students feel stressed about searching for the most comprehensive and detailed NCERT Solutions for Class 7 Maths , we at BYJU’S have prepared step-by-step solutions with detailed explanations. We advise students who want to score good marks in Maths, to go through these solutions and strengthen their knowledge.

Download Exclusively Curated Chapter Notes for Class 7 Maths Chapter – 1 Integers

Download most important questions for class 7 maths chapter – 1 integers.

Chapter 1 – Integers contains 4 exercises, and the NCERT Solutions available on this page provide solutions to the questions present in the exercises. Now, let us have a look at some of the concepts discussed in this chapter.

• Introduction of Integers
• Properties of Addition and Subtraction of Integers
• Multiplication of Integers
• Multiplication of a Positive and Negative Integer
• Multiplication of Two Negative Integer
• Properties of Multiplication of Integers
• Division of Integers
• Properties of Division of Integers

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Exercise 1.1 Solutions

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Exercise 1.1 Page: 4

1. Following number line shows the temperature in degree celsius (c o ) at different places on a particular day.

(a) Observe this number line and write the temperature of the places marked on it.

By observing the number line, we can find the temperature of the cities as follows:

The temperature in Lahulspiti is -8 o C

The temperature in Srinagar is -2 o C

The temperature in Shimla is 5 o C

The temperature in Ooty is 14 o C

The temperature in Bengaluru is 22 o C

(b) What is the temperature difference between the hottest and the coldest places among the above?

From the number line, we observe that

The temperature at the hottest place, i.e., Bengaluru, is 22 o C

The temperature at the coldest place, i.e., Lahulspiti, is -8 o C

Temperature difference between hottest and coldest place is = 22 o C – (-8 o C)

= 22 o C + 8 o C

Hence, the temperature difference between the hottest and the coldest place is 30 o C.

(c) What is the temperature difference between Lahulspiti and Srinagar?

From the given number line,

∴ The temperature difference between Lahulspiti and Srinagar is = -2 o C – (8 o C)

= – 2 O C + 8 o C

(d) Can we say the temperature of Srinagar and Shimla, taken together, is less than the

temperature in Shimla? Is it also less than the temperature in Srinagar?

The temperature in Srinagar =-2 o C

The temperature in Shimla = 5 o C

The temperature of Srinagar and Shimla, taken together, is = – 2 o C + 5 o C

∴ 5 o C > 3 o C

So, the temperature of Srinagar and Shimla, taken together, is less than the temperature at Shimla.

3 o > -2 o

No, the temperature of Srinagar and Shimla, taken together, is not less than the temperature of Srinagar.

2. In a quiz, positive marks are given for correct answers and negative marks are given

for incorrect answers. If Jack’s scores in five successive rounds were 25, – 5, – 10,

15 and 10, what was his total at the end?

From the question,

Jack’s score in five successive rounds are 25, -5, -10, 15 and 10

The total score of Jack at the end will be = 25 + (-5) + (-10) + 15 + 10

= 25 – 5 – 10 + 15 + 10

∴ Jack’s total score at the end is 35.

3. At Srinagar temperature was – 5°C on Monday, and then it dropped by 2°C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day?

The temperature on Monday in Srinagar = -5 o C

The temperature on Tuesday in Srinagar dropped by 2 o C = Temperature on Monday – 2 o C

= -5 o C – 2 o C

The temperature on Wednesday in Srinagar rose by 4 o C = Temperature on Tuesday + 4 o C

= -7 o C + 4 o C

Thus, the temperature on Tuesday and Wednesday was -7 o C and -3 o C, respectively.

4. A plane is flying at the height of 5000 m above sea level. At a particular point, it is exactly above a submarine floating 1200 m below sea level. What is the vertical distance between them?

The plane is flying at a height = 5000 m

Depth of submarine = -1200 m

The vertical distance between plane and submarine = 5000 m – (- 1200) m

= 5000 m + 1200 m

5. Mohan deposits ₹ 2,000 in his bank account and withdraws ₹ 1,642 from it the next day. If the withdrawal of the amount from the account is represented by a negative integer, then how will you represent the amount deposited? Find the balance in Mohan’s account after the withdrawal.

Withdrawal of the amount from the account is represented by a negative integer.

Then, the deposit of the amount to the account is represented by a positive integer.

Total amount deposited in bank account by the Mohan = ₹ 2000

The total amount withdrawn from the bank account by the Mohan = – ₹ 1642

Balance in Mohan’s account after the withdrawal = amount deposited + amount withdrawn

= ₹ 2000 + (-₹ 1642)

= ₹ 2000 – ₹ 1642

Hence, the balance in Mohan’s account after the withdrawal is ₹ 358.

6. Rita goes 20 km towards the east from point A to point B. From B, she moves 30 km towards the west along the same road. If the distance towards the east is represented by a positive integer, then how will you represent the distance travelled towards the west? By which integer will you represent her final position from A?

From the question, it is given that

A positive integer represents the distance towards the east.

Then, the distance travelled towards the west will be represented by a negative integer.

Rita travels a distance in the east direction = 20 km

Rita travels a distance in the west direction = – 30 km

∴ Distance travelled from A = 20 + (- 30)

Hence, we will represent the distance travelled by Rita from point A by a negative integer, i.e., – 10 km

7. In a magic square, each row, column and diagonal have the same sum. Check which of the following is a magic square .

First, we consider the square (i)

By adding the numbers in each row, we get

= 5 + (- 1) + (- 4) = 5 – 1 – 4 = 5 – 5 = 0

= -5 + (-2) + 7 = – 5 – 2 + 7 = -7 + 7 = 0

= 0 + 3 + (-3) = 3 – 3 = 0

By adding the numbers in each column, we get

= 5 + (- 5) + 0 = 5 – 5 = 0

= (-1) + (-2) + 3 = -1 – 2 + 3 = -3 + 3 = 0

= -4 + 7 + (-3) = -4 + 7 – 3 = -7 + 7 = 0

By adding the numbers in diagonals, we get

= 5 + (-2) + (-3) = 5 – 2 – 3 = 5 – 5 = 0

= -4 + (-2) + 0 = – 4 – 2 = -6

Because the sum of one diagonal is not equal to zero.

So, (i) is not a magic square

Now, we consider the square (ii)

= 1 + (-10) + 0 = 1 – 10 + 0 = -9

= (-4) + (-3) + (-2) = -4 – 3 – 2 = -9

= (-6) + 4 + (-7) = -6 + 4 – 7 = -13 + 4 = -9

= 1 + (-4) + (-6) = 1 – 4 – 6 = 1 – 10 = -9

= (-10) + (-3) + 4 = -10 – 3 + 4 = -13 + 4

= 0 + (-2) + (-7) = 0 – 2 – 7 = -9

= 1 + (-3) + (-7) = 1 – 3 – 7 = 1 – 10 = -9

= 0 + (-3) + (-6) = 0 – 3 – 6 = -9

(ii) square is a magic square because the sum of each row, each column and the diagonal is equal to -9.

8. Verify a – (– b) = a + b for the following values of a and b.

(i) a = 21, b = 18

a = 21 and b = 18

To verify a – (- b) = a + b

Let us take Left Hand Side (LHS) = a – (- b)

= 21 – (- 18)

Now, Right Hand Side (RHS) = a + b

By comparing LHS and RHS

Hence, the value of a and b is verified.

(ii) a = 118, b = 125

a = 118 and b = 125

= 118 – (- 125)

= 118 + 125

By comparing LHS and RHS,

(iii) a = 75, b = 84

a = 75 and b = 84

= 75 – (- 84)

(iv) a = 28, b = 11

a = 28 and b = 11

= 28 – (- 11)

9. Use the sign of >, < or = in the box to make the statements true.

(a) (-8) + (-4) [ ] (-8) – (-4)

Let us take Left Hand Side (LHS) = (-8) + (-4)

Now, Right Hand Side (RHS) = (-8) – (-4)

LHS < RHS

-12 < -4

∴ (-8) + (-4) [<] (-8) – (-4)

(b) (-3) + 7 – (19) [ ] 15 – 8 + (-9)

Let us take Left Hand Side (LHS) = (-3) + 7 – 19

= -3 + 7 – 19

Now, Right Hand Side (RHS) = 15 – 8 + (-9)

= 15 – 8 – 9

-15 < -2

∴ (-3) + 7 – (19) [<] 15 – 8 + (-9)

(c) 23 – 41 + 11 [ ] 23 – 41 – 11

Let us take Left Hand Side (LHS) = 23 – 41 + 11

= 34 – 41

= – 7

Now, Right Hand Side (RHS) = 23 – 41 – 11

= 23 – 52

= – 29

LHS > RHS

– 7 > -29

∴ 23 – 41 + 11 [>] 23 – 41 – 11

(d) 39 + (-24) – (15) [ ] 36 + (-52) – (- 36)

Let us take Left Hand Side (LHS) = 39 + (-24) – 15

= 39 – 24 – 15

Now, Right Hand Side (RHS) = 36 + (-52) – (- 36)

= 36 – 52 + 36

∴ 39 + (-24) – (15) [<] 36 + (-52) – (- 36)

(e) – 231 + 79 + 51 [ ] -399 + 159 + 81

Let us take Left Hand Side (LHS) = – 231 + 79 + 51

= – 231 + 130

Now, Right Hand Side (RHS) = – 399 + 159 + 81

= – 399 + 240

= – 159

-101 > -159

∴ – 231 + 79 + 51 [>] -399 + 159 + 81

10. A water tank has steps inside it. A monkey is sitting on the topmost step (i.e., the first step). The water level is at the ninth step.

(i) He jumps 3 steps down and then jumps back 2 steps up. In how many jumps will he reach the water level?

Let us consider steps moved down are represented by positive integers, and then steps moved up are represented by negative integers.

Initially, the monkey is sitting on the topmost step, i.e., the first step

In 1 st jump, the monkey will be at step = 1 + 3 = 4 steps

In 2 nd jump, the monkey will be at step = 4 + (-2) = 4 – 2 = 2 steps

In 3 rd jump, the monkey will be at step = 2 + 3 = 5 steps

In 4 th jump, the monkey will be at step = 5 + (-2) = 5 – 2 = 3 steps

In 5 th jump, the monkey will be at step = 3 + 3 = 6 steps

In 6 th jump, the monkey will be at step = 6 + (-2) = 6 – 2 = 4 steps

In 7 th jump, the monkey will be at step = 4 + 3 = 7 steps

In 8 th jump, the monkey will be at step = 7 + (-2) = 7 – 2 = 5 steps

In 9 th jump, the monkey will be at step = 5 + 3 = 8 steps

In 10 th jump, the monkey will be at step = 8 + (-2) = 8 – 2 = 6 steps

In 11 th jump, the monkey will be at step = 6 + 3 = 9 steps

∴ The monkey took 11 jumps (i.e., the 9 th step) to reach the water level.

(ii) After drinking water, he wants to go back. For this, he jumps 4 steps up and then jumps back 2 steps down with every move. In how many jumps will he reach back to the top step?

Initially, the monkey is sitting on the ninth step, i.e., at the water level,

In 1 st jump, the monkey will be at step = 9 + (-4) = 9 – 4 = 5 steps

In 2 nd jump, the monkey will be at step = 5 + 2 = 7 steps

In 3 rd jump, the monkey will be at step = 7 + (-4) = 7 – 4 = 3 steps

In 4 th jump, the monkey will be at step = 3 + 2 = 5 steps

In 5 th jump, the monkey will be at step = 5 + (-4) = 5 – 4 = 1 step

∴ The monkey took 5 jumps to reach back to the top step, i.e., the first step.

(iii) If the number of steps moved down is represented by negative integers, and the number of steps moved up by positive integers, represent his moves in parts (i) and (ii) by completing the following: (a) – 3 + 2 – … = – 8 (b) 4 – 2 + … = 8. In (a), the sum (– 8) represents going down by eight steps. So, what will the sum 8 in (b) represent?

The number of steps moved down is represented by negative integers, and the number of steps moved up by positive integers.

Monkey moves in part (i)

= – 3 + 2 – ……….. = – 8

Then, LHS = – 3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3 + 2 – 3

= – 18 + 10

= – 8

∴ Moves in part (i) represent the monkey going down 8 steps because it’s a negative integer.

Monkey moves in part (ii)

= 4 – 2 + ……….. = 8

Then, LHS = 4 – 2 + 4 – 2 + 4

= 12 – 4

∴ Moves in part (ii) represent the monkey going up 8 steps because it’s a positive integer.

Exercise 1.2 Page: 9

1. Write down a pair of integers whose:

(a) sum is -7

= – 4 + (-3)

(b) the difference is – 10

= -25 – (-15)

(c) sum is 0

2. (a) Write a pair of negative integers whose difference gives 8

= (-5) – (- 13)

(b) Write a negative integer and a positive integer whose sum is – 5.

(c) Write a negative integer and a positive integer whose difference is – 3.

Solution :-

= – 2 – (1)

= – 2 – 1

= – 3

3. In a quiz, team A scored – 40, 10, 0 and team B scored 10, 0, – 40 in three successive rounds. Which team scored more? Can we say that we can add integers in any order?

The score of team A = -40, 10, 0

Total score obtained by team A = – 40 + 10 + 0

= – 30

The score of team B = 10, 0, -40

Total score obtained by team B = 10 + 0 + (-40)

= 10 + 0 – 40

Thus, the score of both the A team and B team is the same.

Yes, we can say that we can add integers in any order.

4. Fill in the blanks to make the following statements true.

(i) (–5) + (– 8) = (– 8) + (…………)

Let us assume the missing integer be x,

= (–5) + (– 8) = (– 8) + (x)

= – 5 – 8 = – 8 + x

= – 13 = – 8 + x

By sending – 8 from RHS to LHS, it becomes 8

= – 13 + 8 = x

= x = – 5

Now, substitute the x value in the blank place.

(ii) –53 + ………… = –53

= –53 + x = –53

By sending – 53 from LHS to RHS, it becomes 53

= x = -53 + 53

(iii) 17 + ………… = 0

= 17 + x = 0

By sending 17 from LHS to RHS, it becomes -17

= x = 0 – 17

= x = – 17

= 17 – 17 = 0

(iv) [13 + (– 12)] + (…………) = 13 + [(–12) + (–7)]

= 1 + (x) = 13 – 19

= 1 + (x) = -6

By sending 1 from LHS to RHS, it becomes -1.

= x = -6 – 1

(v) (– 4) + [15 + (–3)] = [– 4 + 15] +…………

Let us assume the missing integer be x.

= (– 4) + [15 + (–3)] = [– 4 + 15] + x

= (– 4) + [15 – 3)] = [– 4 + 15] + x

= (-4) + [12] = [11] + x

= 8 = 11 + x

By sending 11 from RHS to LHS, it becomes -11,

= 8 – 11 = x

Exercise 1.3 Page: 21

1. Find each of the following products:

(a) 3 × (–1)

By the rule of Multiplication of integers,

(b) (–1) × 225

= (-1) × 225

(c) (–21) × (–30)

= (-21) × (-30)

(d) (–316) × (–1)

= (-316) × (-1)

(e) (–15) × 0 × (–18)

= (–15) × 0 × (–18)

∵ If any integer is multiplied by zero, the answer is zero itself.

(f) (–12) × (–11) × (10)

= (–12) × (-11) × (10)

First, multiply the two numbers having the same sign.

(g) 9 × (–3) × (– 6)

= 9 × (-3) × (-6)

(h) (–18) × (–5) × (– 4)

= (-18) × (-5) × (-4)

(i) (–1) × (–2) × (–3) × 4

= – 24

(j) (–3) × (–6) × (–2) × (–1)

= 18 × 2 … [∵ (- × – = +)

2. Verify the following:

(a) 18 × [7 + (–3)] = [18 × 7] + [18 × (–3)]

From the given equation,

Hence, the given equation is verified.

(b) (–21) × [(– 4) + (– 6)] = [(–21) × (– 4)] + [(–21) × (– 6)]

3. (i) For any integer a, what is (–1) × a equal to?

= (-1) × a = -a

When we multiply any integer a with -1, then we get the additive inverse of that integer.

(ii). Determine the integer whose product with (–1) is

Now, multiply -22 with (-1), and we get

= -22 × (-1)

When we multiply integer -22 with -1, then we get the additive inverse of that integer.

Now, multiply 37 with (-1), and we get

= 37 × (-1)

When we multiply integer 37 with -1, then we get the additive inverse of that integer.

Now, multiply 0 by (-1), and we get

Because the product of negative integers and zero gives zero only.

4. Starting from (–1) × 5, write various products showing some pattern to show

(–1) × (–1) = 1.

The various products are,

= -1 × 5 = -5

= -1 × 4 = -4

= -1 × 3 = -3

= -1 × 2 = -2

= -1 × 1 = -1

= -1 × 0 = 0

= -1 × -1 = 1

We concluded that the product of one negative integer and one positive integer is a negative integer. Then, the product of two negative integers is a positive integer.

5. Find the product using suitable properties:

(a) 26 × (– 48) + (– 48) × (–36)

The given equation is in the form of the Distributive Law of Multiplication over Addition.

= a × (b + c) = (a × b) + (a × c)

Let, a = -48, b = 26, c = -36

= 26 × (– 48) + (– 48) × (–36)

= -48 × (26 + (-36)

= -48 × (26 – 36)

= -48 × (-10)

= 480 … [∵ (- × – = +)

(b) 8 × 53 × (–125)

The given equation is in the form of the Commutative Law of Multiplication.

= a × b = b × a

= [8 × (-125)] × 53

= [-1000] × 53

= – 53000

(c) 15 × (–25) × (– 4) × (–10)

= 15 × [(–25) × (– 4)] × (–10)

= 15 × [100] × (–10)

= – 15000

(d) (– 41) × 102

= (-41) × (100 + 2)

= (-41) × 100 + (-41) × 2

= – 4100 – 82

= – 4182

(e) 625 × (–35) + (– 625) × 65

= – 62500

(f) 7 × (50 – 2)

The given equation is in the form of the Distributive Law of Multiplication over Subtraction.

= a × (b – c) = (a × b) – (a × c)

= (7 × 50) – (7 × 2)

(g) (–17) × (–29)

(h) (–57) × (–19) + 57

= (57 × 19) + (57 × 1)

6. A certain freezing process requires that room temperature be lowered from 40°C at the rate of 5°C every hour. What will be the room temperature 10 hours after the process begins?

Let us take the lowered temperature as negative.

Initial temperature = 40 o C

Change in temperature per hour = -5 o C

Change in temperature after 10 hours = (-5) × 10 = -50 o C

∴ The final room temperature after 10 hours of freezing process = 40 o C + (-50 o C)

7. In a class test containing 10 questions, 5 marks are awarded for every correct answer and (–2) marks are awarded for every incorrect answer and 0 for questions not attempted.

(i) Mohan gets four correct and six incorrect answers. What is his score?

Marks awarded for 1 correct answer = 5

Total marks awarded for 4 correct answer = 4 × 5 = 20

Marks awarded for 1 wrong answer = -2

Total marks awarded for 6 wrong answer = 6 × -2 = -12

∴ Total score obtained by Mohan = 20 + (-12)

(ii) Reshma gets five correct answers and five incorrect answers; what is her score?

Total marks awarded for 5 correct answer = 5 × 5 = 25

Total marks awarded for 5 wrong answer = 5 × -2 = -10

∴ Total score obtained by Reshma = 25 + (-10)

(iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?

Total marks awarded for 2 correct answer = 2 × 5 = 10

Marks awarded for questions not attempted is = 0

∴ Total score obtained by Heena = 10 + (-10)

8. A cement company earns a profit of ₹ 8 per bag of white cement sold and a loss of

₹ 5 per bag of grey cement sold.

(a) The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss?

We denote profit in a positive integer and loss in a negative integer,

The cement company earns a profit on selling 1 bag of white cement = ₹ 8 per bag

The cement company earns a profit on selling 3000 bags of white cement = 3000 × ₹ 8

Loss on selling 1 bag of grey cement = – ₹ 5 per bag

Loss on selling 5000 bags of grey cement = 5000 × – ₹ 5

= – ₹ 25000

Total loss or profit earned by the cement company = profit + loss

= 24000 + (-25000)

= – ₹1000

Thus, a loss of ₹ 1000 will be incurred by the company.

(b) What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6,400 bags?

Let the number of white cement bags be x.

Cement company earns a profit on selling x bags of white cement = (x) × ₹ 8

Loss on selling 6400 bags of grey cement = 6400 × – ₹ 5

= – ₹ 32000

According to the question,

The company must sell to have neither profit nor loss.

= profit + loss = 0

= 8x + (-32000) =0

By sending -32000 from LHS to RHS, it becomes 32000

= 8x = 32000

= x = 32000/8

Hence, the 4000 bags of white cement have neither profit nor loss.

9. Replace the blank with an integer to make it a true statement.

(a) (–3) × _____ = 27

= (–3) × (x) = 27

= x = – (27/3)

Let us substitute the value of x in the place of blank,

(b) 5 × _____ = –35

= (5) × (x) = -35

= x = – (-35/5)

Let us substitute the value of x in the place of the blank.

(c) _____ × (– 8) = –56

= (x) × (-8) = -56

= x = (-56/-8)

(d) _____ × (–12) = 132

= (x) × (-12) = 132

= x = – (132/12)

= x = – 11

Exercise 1.4 Page: 26

1. Evaluate each of the following.

(a) (–30) ÷ 10

= (–30) ÷ 10

When we divide a negative integer by a positive integer, we first divide them as whole numbers and then put the minus sign (-) before the quotient.

(b) 50 ÷ (–5)

= (50) ÷ (-5)

= – 10

When we divide a positive integer by a negative integer, we first divide them as whole numbers and then put the minus sign (-) before the quotient.

(c) (–36) ÷ (–9)

= (-36) ÷ (-9)

When we divide a negative integer by a negative integer, we first divide them as whole numbers and then put the positive sign (+) before the quotient.

(d) (– 49) ÷ (49)

= (–49) ÷ 49

= – 1

(e) 13 ÷ [(–2) + 1]

= 13 ÷ (-1)

= – 13

(f) 0 ÷ (–12)

= 0 ÷ (-12)

When we divide zero by a negative integer, it gives zero.

(g) (–31) ÷ [(–30) + (–1)]

= (-31) ÷ (-31)

(h) [(–36) ÷ 12] ÷ 3

First, we have to solve the integers within the bracket.

= (–36) ÷ 12

(i) [(– 6) + 5)] ÷ [(–2) + 1]

The given question can be written as,

2. Verify that a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) for each of the following values of a, b and c.

(a) a = 12, b = – 4, c = 2

From the question, a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)

Given, a = 12, b = – 4, c = 2

Now, consider LHS = a ÷ (b + c)

= 12 ÷ (-4 + 2)

= 12 ÷ (-2)

Then, consider RHS = (a ÷ b) + (a ÷ c)

= (12 ÷ (-4)) + (12 ÷ 2)

= (-3) + (6)

= LHS ≠ RHS

Hence, the given values are verified.

(b) a = (–10), b = 1, c = 1

Given, a = (-10), b = 1, c = 1

= (-10) ÷ (1 + 1)

= (-10) ÷ (2)

= ((-10) ÷ (1)) + ((-10) ÷ 1)

= (-10) + (-10)

3. Fill in the blanks:

(a) 369 ÷ _____ = 369

= 369 ÷ x = 369

= x = (369/369)

Now, put the valve of x in the blank.

= 369 ÷ 1 = 369

(b) (–75) ÷ _____ = –1

= (-75) ÷ x = -1

= x = (-75/-1)

= (-75) ÷ 75 = -1

(c) (–206) ÷ _____ = 1

= (-206) ÷ x = 1

= x = (-206/1)

= (-206) ÷ (-206) = 1

(d) – 87 ÷ _____ = 87

= (-87) ÷ x = 87

= x = (-87)/87

= (-87) ÷ (-1) = 87

(e) _____ ÷ 1 = – 87

= (x) ÷ 1 = -87

= x = (-87) × 1

= (-87) ÷ 1 = -87

(f) _____ ÷ 48 = –1

= (x) ÷ 48 = -1

= x = (-1) × 48

= (-48) ÷ 48 = -1

(g) 20 ÷ _____ = –2

= 20 ÷ x = -2

= x = (20)/ (-2)

= (20) ÷ (-10) = -2

(h) _____ ÷ (4) = –3

= (x) ÷ 4 = -3

= x = (-3) × 4

= (-12) ÷ 4 = -3

4. Write five pairs of integers (a, b) such that a ÷ b = –3. One such pair is (6, –2) because 6 ÷ (–2) = (–3).

(i) (15, -5)

Because, 15 ÷ (–5) = (–3)

(ii) (-15, 5)

Because, (-15) ÷ (5) = (–3)

(iii) (18, -6)

Because, 18 ÷ (–6) = (–3)

(iv) (-18, 6)

Because, (-18) ÷ 6 = (–3)

(v) (21, -7)

Because, 21 ÷ (–7) = (–3)

5. The temperature at 12 noon was 10 o C above zero. If it decreases at the rate of 2 o C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at midnight?

From the question, it is given,

The temperature at the beginning, i.e., at 12 noon = 10 o C

Rate of change of temperature = – 2 o C per hour

Temperature at 1 PM = 10 + (-2) = 10 – 2 = 8 o C

Temperature at 2 PM = 8 + (-2) = 8 – 2 = 6 o C

Temperature at 3 PM = 6 + (-2) = 6 – 2 = 4 o C

Temperature at 4 PM = 4 + (-2) = 4 – 2 = 2 o C

Temperature at 5 PM = 2 + (-2) = 2 – 2 = 0 o C

Temperature at 6 PM = 0 + (-2) = 0 – 2 = -2 o C

Temperature at 7 PM = -2 + (-2) = -2 -2 = -4 o C

Temperature at 8 PM = -4 + (-2) = -4 – 2 = -6 o C

Temperature at 9 PM = -6 + (-2) = -6 – 2 = -8 o C

∴ At 9 PM, the temperature will be 8 o C below zero.

The temperature at midnight, i.e., at 12 AM

Change in temperature in 12 hours = -2 o C × 12 = – 24 o C

So, at midnight temperature will be = 10 + (-24)

= – 14 o C

So, at midnight, the temperature will be 14 o C below 0.

6. In a class test, (+ 3) marks are given for every correct answer and (–2) marks are given for every incorrect answer and no marks for not attempting any question. (i) Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly? (ii) Mohini scored –5 marks on this test, though she got 7 correct answers. How many questions has she attempted incorrectly?

Marks awarded for 1 correct answer = + 3

(i) Radhika scored 20 marks.

Total marks awarded for 12 correct answers = 12 × 3 = 36

Marks awarded for incorrect answers = Total score – Total marks awarded for 12 correct

= – 16

So, the number of incorrect answers made by Radhika = (-16) ÷ (-2)

(ii) Mohini scored -5 marks.

Total marks awarded for 7 correct answers = 7 × 3 = 21

= – 5 – 21

= – 26

So, the number of incorrect answers made by Mohini = (-26) ÷ (-2)

7. An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 10 m above the ground level, how long will it take to reach – 350 m?

The initial height of the elevator = 10 m

The final depth of the elevator = – 350 m … [∵distance descended is denoted by a negative

The total distance to descended by the elevator = (-350) – (10)

= – 360 m

Time taken by the elevator to descend -6 m = 1 min

So, the time taken by the elevator to descend – 360 m = (-360) ÷ (-6)

= 60 minutes

Disclaimer:

Dropped Topics – Introduction, Recall, 1.4.3 Product of three or more negative numbers and 1.5.7 Making multiplication easier.

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• NCERT Class 7 Maths Book PDF
• NCERT Books

CBSE Class 7 NCERT Maths Books Free Download

NCERT books are an integral part of the curriculum of any CBSE school. The students prefer these books because they find them easier to study owing to their simplicity. PDF versions of these texts and its related materials are also readily available. NCERT books for Class 7 Maths, is no exception.

Students can download the PDF and access it from anywhere. They can use the solutions to the Class 7th NCERT Maths book and understand the concepts better. NCERT Maths Class 7 textbook is ideal for young students because these books would enable them to understand each of the topics comprehensively.

These NCERT Solutions help students in learning the concept in a comprehensive manner and allow them to score better marks in their Examination.

NCERT Books For Class 7 Maths; Free PDF Download

The NCERT Book for Class 7 Maths provides clear explanations, solved examples, and practice exercises to enhance conceptual understanding and problem-solving skills. You can download the NCERT Book for Class 7 Maths in both English and Hindi Languages. Get the link to download Maths Class 7, NCERT Books from the table below.

NCERT Solutions for Class 7 Maths | Chapterwise PDF

NCERT Books for Class 7

Ncert solutions for class 7, ncert books for class 7 maths pdf - free download.

Class 7 is crucial for pupils because it provides them with a solid foundation in all of the fundamental topics and aids in their overall development. The NCERT book for Class 7 Maths is crucial for CBSE Class 7 students since it provides a comprehensive review of the whole topic that is taught according to the syllabus. If a student wants to be at the top of his or her Class, self-study is just as vital as regular lessons. The NCERT Class 7 Maths book comes in handy here. NCERT books are typically written by subject specialists with the goal of assisting students in understanding concepts from the most basic to the most complex. These books break down Maths problems into easy-to-understand steps.

For the convenience of the students, NCERT books for Class 7 Maths are provided here. The National Council of Educational Research and Training (NCERT) created the book in accordance with the CBSE's most recent syllabus. CBSE has prescribed the NCERT Maths book for students in affiliated schools in Class 7. Students are exposed to a range of themes in Class 7 Maths, such as Practical Geometry, Data Processing, Rational Numbers, and so on, which are necessary not only for Examinations but also for understanding complicated issues in later Classes. It is also necessary to be able to answer these problems quickly in order to have a good understanding of the Mathematical challenges. You can discover a selection of NCERT answers for Class 7 Maths below, which will certainly help you improve your test score.

Maths has always been a difficult subject to grasp and master. To be able to answer Mathematical issues in the simplest yet most effective way, it is necessary to have a solid comprehension of the many themes as well as the numerous formulae. The capacity to answer complicated Mathematics in the future can only be attributed to the fact that issues may be solved at an earlier and younger level. A person's Mathematics solving abilities will only grow if they can answer issues based on a few practice questions and grasp Examples of solved problems.

The textbooks provided here can be downloaded and utilised at one's leisure. Aside from textbooks, students are given NCERT solutions to help them resolve any issues they may have when doing the practice problems. Any kid who prepares from NCERT books for Class 7 Maths will be able to study for their major Maths test and perform to the best of their abilities. The whole CBSE Class 7 Maths book is freely accessible and may be downloaded in PDF format.

The Class 7 Maths NCERT Book has a total of 15 Chapters. The majority of the Chapters are simple to comprehend and solve. Only a few Chapters, such as Chapter 6 – Triangles and Their Properties, Chapter 7 – Triangle Congruence, Chapter 10 Practical Geometry, and Chapter 12 Algebraic Expressions, require extra practice to be confident. Regular arithmetic practice makes it easier than before.

Nowadays, online assistance is prevalent. In Class 7, try to devote at least two hours to Maths. Use internet tools and applications to help you practise each of your exercises. If a kid does Maths for 1 to 2 hours every day, he will be able to complete the whole 7th Maths syllabus for 2024-25 in three or four months. Later on, he must rewrite just during the academic session's break.

There are numerous Chapters in 7th Mathematics that are rather simple to solve. Simply practise these Chapters to get a higher score in less time. Chapters 3, 4, 11, 13, 14, and 15 in Class 7 Maths, for Example, are easier to grasp and practise. So focus on Chapters like these to achieve high marks in 7th-grade Maths in order to pass the tests in 30 days.

Class 7 Math NCERT Books include Chapters that correspond to the most recent CBSE Syllabus for 2024-25. The majority of the Chapters are simple to practise and solve. Only a few are regarded as challenging. Passing 7th Maths, on the other hand, is a piece of cake. Just by covering the curriculum and executing simple Chapters correctly, a student can pass 7th Maths with a reasonable grade. If a student wants to achieve in standard 7th Maths, he must put in the effort.

You may download whole books in PDF format or download individual Chapters in each subject. Download PDFs of Maths, Science, Social Science (SST), English, and Hindi books directly from Vedantu. These books are intended for All-State Board students as well as CBSE pupils.

Along with the book, the NCERT Class 7 Maths Solutions are also important for practice. NCERT solutions for Class 7 Maths include solutions and analyses for all NCERT textbook sums based on triangles, area, and perimeter of various forms, data management, integers, and so on. These NCERT answers for Class 7 Mathematics have been developed by Maths gurus to appeal to children of all cognitive levels. As a result, CBSE pupils benefit from the development of auxiliary skills and Mathematical aptitude.

NCERT answers for Class 7 Maths are incredibly beneficial to students studying for both home and competitive Exams. These solutions provide pupils in grade 7 the opportunity to build a solid grasp of Mathematics. CBSE NCERT textbooks for Class 7 Maths are extremely crucial and may also be utilized by aspirants from other boards who desire to have rock-solid Mathematical knowledge.

The greatest and most exact strategies are used to explain NCERT Solutions for Class 7 Maths. These free PDF downloads of Chapter-by-Chapter analysis of problems are available. The links to all of the solutions are provided on Vedantu, depending on the topic you're studying.

It is critical to revisit the solutions on a regular basis to ensure that you are well-versed in all areas at the time of an Examination. These NCERT answers for Class 7 Maths help students have a better knowledge of the subject.

On test days, students find it quite difficult to answer all of the questions. Students require a rapid run-through of all problems since each sum is equally essential. The concepts mentioned in the NCERT book for Class 7 must be understood well and notes must be made by the students. These notes can help recall a step-by-step, in-depth study of all issues. Students may browse through these and review how to answer each question quickly.

When a student attempts to answer a textbook problem, he may not be able to complete it entirely. This might be the result of a blunder or a faulty premise. NCERT answers for Class 7 Maths are exact and well-explained, removing any questions a learner may have.

Algebra, general Maths, and Geometry are all covered in the NCERT Class 7 Maths Book. Integers, data processing, basic equations, lines and angles, and many other topics were covered in the Chapters, which aimed to improve students' understanding of the subject. Mathematics is said to open up numerous chances for kids in the future if they have a good knowledge and firm grip of it.

The language in this book has been kept as simple as possible to aid students in gaining a thorough knowledge of the subject. It is critical to complete as many activities as possible in order to have a thorough grasp of each Chapter. This book aims to help students prepare for the National Talent Search Examination, which is administered by NCERT.

The book has a large number of activities for students to do, and it has been made engaging with photos, drawings, and other elements, guaranteeing that students have a positive learning experience. The book's major goal is to familiarise every student with the fundamentals of each Chapter so that, if a new type of question arises from the Chapter, the students can readily respond.

Each Chapter has a blue box labeled "Try These," which provides intriguing information or challenging questions to answer. These are extra facts or questions that will only add to the student's knowledge of the subject. Each Chapter has a number of questions that students must answer in order to fully comprehend the topic.

It has been noted that the majority of students are afraid or weak in the subject of Mathematics, owing to a lack of formation of a firm foundation from the very early stages of learning. NCERT works on this element and helps students build a good grasp of each Chapter by offering several activities with a variety of questions to assist them to overcome their phobia of this topic.

NCERT books are well-known for presenting ideas in the simplest way possible so that students may grasp them fast. As a result, students are constantly pushed to study NCERT books in order to achieve in their studies. We are presenting the NCERT book on Maths to students in Class 7. This is the most recent version of the NCERT book, which was released at the start of the last academic session by the National Council for Educational Research and Training (NCERT). This new NCERT book on Class 7 Maths explains all ideas and theorems in a clear and concise manner, making learning simple and effective.

Other Free CBSE Class 7 Maths Study Material

Other Free Study CBSE Material for Class 7

FAQs on NCERT Class 7 Maths Book PDF

1. How many chapters are there in the NCERT Books for Class 7 Maths?

There are a total of 15 chapters in the NCERT Books for Class 7 Maths. Below are the names of the chapters: 

Chapter 1 - Integers

Chapter 2 - Fractions and Decimals

Chapter 3 - Data Handling

Chapter 4 - Simple Equations

Chapter 5 - Lines and Angles

Chapter 6 - Lines and Angles

Chapter 7 - The Triangle and Its Properties

Chapter 8 - Congruence of Triangles

Chapter 9 - Comparing Quantities

Chapter 10 - Rational Numbers

Chapter 11 - Practical Geometry

Chapter 12 - Perimeter and Area

Chapter 13 - Algebraic Expression

Chapter 14 - Exponents and Power

Chapter 15 - Symmetry

Chapter 16 - Visualising Solid Shape

2. What is the sixth chapter of Class 7 Maths NCERT textbook all about?

The sixth chapter of Class 7 Maths NCERT textbook depicts The Triangle and its Properties. After Chapter 5 Lines and Angles, this is the second chapter related to Geometry in NCERT 7th maths textbook. This chapter is all about triangles.

It includes an in-depth discussion regarding various types of triangles. There is an elaborate discussion on the properties of triangles, which enable students to have a clear concept of this topic. In this chapter, the students will also learn the concepts of altitude of triangles and exterior angles. Moreover, students will get an introduction of the two specialised sub-types of triangles: equilateral and isosceles. They will also learn about the Pythagorean Theory, which will be helpful in their higher studies too.

3. What are the benefits of referring to the Class 7 Maths NCERT textbook?

Maths is a very important subject. To hold strong command over the fundamental concepts of each topic, every student should practise the problems of Mathematics very well. They can also take help from the NCERT books for class 7 Maths and the solutions of it which are available online. These books introduce a Class 7 student to some critical concepts like that of Arithmetic, Algebra, and Geometry.

NCERT books are an integral part of the curriculum of any CBSE school. The students prefer these books because they find them easier to study owing to its simplicity. NCERT books for class 7 maths is no exception. NCERT maths class 7 textbook is ideal for young students because these books would enable them to understand each of the topics comprehensively.

4. How can I download the NCERT Books for Class 7 Maths?

Students can download the PDF of NCERT Books for Class 7 Maths and access it from anywhere, be it the official website of NCERT or the official site of Vedantu. One can also download it from Vedantu app as well. In that case, they have to download the app on their phone or any smart device beforehand. These NCERT books are accessible for absolutely free of cost.

The NCERT Book for Class 7 Maths is beneficial to students since it provides them with an in-depth understanding of the topic. They can also look through to clear up any Class 7 Maths confusions they may have:

Prepared by topic matter experts

Provides detailed information about the subject

Even the most complicated ideas have simple step-by-step answers.

Prepare well for Class 7 Examinations.

Practice tackling Class 7 Maths problems at home.

Visit Vedantu for additional test resources and CBSE notes for Class 7 Maths. Different modules are available free of cost on the Vedantu site.

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By Simon J. Levien and Maggie Astor

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Class 7 Mathematics Rational Numbers Assignments

We have provided below free printable Class 7 Mathematics Rational Numbers Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 7 Mathematics Rational Numbers . These Assignments for Grade 7 Mathematics Rational Numbers cover all important topics which can come in your standard 7 tests and examinations. Free printable Assignments for CBSE Class 7 Mathematics Rational Numbers , school and class assignments, and practice test papers have been designed by our highly experienced class 7 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Rational Numbers Class 7 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Rational Numbers Class 7. Students can click on the links below and download all Pdf Assignments for Mathematics Rational Numbers class 7 for free. All latest Kendriya Vidyalaya Class 7 Mathematics Rational Numbers Assignments with Answers and test papers are given below.

Mathematics Rational Numbers Class 7 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 7 Mathematics Rational Numbers . Students and teachers can download and save all free Mathematics Rational Numbers assignments in Pdf for grade 7th. Our expert faculty have covered Class 7 important questions and answers for Mathematics Rational Numbers as per the latest syllabus for the current academic year. All test papers and question banks for Class 7 Mathematics Rational Numbers and CBSE Assignments for Mathematics Rational Numbers Class 7 will be really helpful for standard 7th students to prepare for the class tests and school examinations. Class 7th students can easily free download in Pdf all printable practice worksheets given below.

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