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Integers Class 7 Notes CBSE Maths Chapter 1 (Free PDF Download)

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Last updated date: 17th Apr 2024
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MVSAT 2024

Exam - Focused Revision Notes for CBSE Class 7 Maths Chapter 1 - Integers

CBSE Class 7 Maths Chapter 1 introduces some of the fundamental concepts of integers. It is very important to get a good understanding of these elementary concepts of integers as students will come across their applications in the other chapters of Mathematics as well. These notes on Integers are prepared by our subject experts in reference to the NCERT textbook.


Students can download and refer to these CBSE Class 7 Maths Chapter 1 revision notes PDF for free from Vedantu. Important concepts like whole numbers, natural numbers, properties of addition and subtraction of integers, number line, etc. are explained in this chapter.


In the fascinating world of mathematics, integers play a crucial role in solving a variety of problems. Understanding the concept of integers is essential for building a strong foundation in mathematics. In this comprehensive set of Class 7 Maths Integers revision notes, provided by Vedantu, we delve into the key aspects of integers, exploring their properties, operations and real-life applications. Let's embark on this journey of discovery and mastery of integers!


Important Topics covered in CBSE Class 7 Maths Chapter 1 Integers

What are Integers?

  • Definition and examples of integers.

  • Differentiating between positive and negative integers.

  • Understanding the number line representation of integers.

Properties of Integers:

  • Closure property: Addition, subtraction and multiplication of integers.

  • Commutative and associative properties.

  • Identity and inverse properties.

  • Distributive property of multiplication over addition/subtraction.

Operations with Integers:

  • Addition and subtraction of integers.

  • Rules for adding and subtracting positive and negative integers.

  • Multiplication and division of integers.

  • Multiplication rules involving positive and negative integers.

Applications of Integers:

  • Real-life scenarios involving integers.

  • Integer operations in solving practical problems.

  • Understanding the concept of absolute value.

Number Patterns and Integers:

  • Recognizing patterns in integer sequences.

  • Identifying arithmetic and geometric progressions.

  • Solving problems using number patterns and sequences.

Simplification of Expressions:

  • Simplifying expressions involving integers.

  • Applying the order of operations (BODMAS/PEMDAS) to solve complex expressions.

Solving Equations with Integers:

  • Solving linear equations involving integers.

  • Equations with multiple operations.

  • Application of equations in problem-solving.

Word Problems:

  • Translating real-life problems into mathematical expressions.

  • Strategies to solve word problems using integers.


Download CBSE Class 7 Maths Revision Notes 2024-25 PDF

Also, check CBSE Class 7 Maths revision notes for All chapters:


Access Class 7 Maths Chapter 1 Integers

Definition of Integers

(i) All whole numbers and their negatives form the set of numbers which represent integers.

(ii) The whole numbers are those numbers which contain $\text{0}$. So, we can represent integers as $...,-2,-1,0,1,2,...$.


Representation on the Number Line

Let us recall how to represent integers on a number line, add and subtract them by considering the examples.

(i) Integers $-3$ and $4$ can be represented on the number line as shown below:


Number line

(ii) Addition of integers is performed as below:

$2+3=5$ 

$(-3)+(-4)=-7$ 

$-10+1=-9$ 

(iii) Subtraction of integers is performed as below:

\[2-3=-1\] 

$(-3)-(-4)=1$ 

$(-4)-10=-14$ 


Properties of Addition and Subtraction of Integers

Let us look at the properties satisfied by addition and subtraction of integers.

(a) Integers are closed for both addition and subtraction. It means that if $a$ and $b$ are integers, then \[a+b\] and $a-b$ are also integers.

(b) Addition is commutative for integers. For all integers $a$ and $b$, $a+b=b+a$.

(c) Addition is associative for integers. For all integers $a$, $b$ and $c$, $\left( a+b \right)+c=a+\left( b+c \right)$.

(d) Adding the integer \[0\] to any integer $a$ results in the integer $a$, i.e., $a+0=a=0+a$. So, we can say that $0$ is the additive identity for integers.


Multiplication of Integers

We learnt how to multiply integers, both positive and negative integers. The following are the examples :

(i) When a positive and a negative integer are multiplied, the result is a negative integer. For example, $-6\times 2=-12$ .

(ii) When two negative integers or two positive integers are multiplied, the result is a positive integer. For example, $-5\times -3=15$ and $6\times 3=18$.

(iii) When an even number of negative integers are multiplied together, the result is positive. For example, $-2\times -3\times -4\times -5=120$.

(iv) When an odd number of negative integers is multiplied together, the result is negative. For example, $-2\times -3\times -4=-24$.


Properties of Multiplication of Integers

Let us look at the properties satisfied by multiplication of integers.

(a) Integers are closed under multiplication. For any two integers $a$ and $b$, $a\times b$ is also an integer.

(b) Multiplication is commutative for integers. For any two integers $a$ and $b$, $a\times b=b\times a$.

(c) Multiplication is associative for integers. For any three integers $a$, \[b\] and $c$, \[\left( a\times b \right)\times c=a\times \left( b\times c \right)\].

(d) Any integer $a$ multiplied by the integer $1$ gives the integer $a$. So, we can say that $1$ is the multiplicative identity of integers. 


Distributive Property

When a factor is multiplied by the sum or addition of two terms, the distributive property states that it is necessary to multiply each of the two integers by the factor before performing the addition or subtraction operation

For any three integers $a,b$ and $c$, \[a\times \left( b+c \right)=a\times b+a\times c\].

or  \[a\times \left( b-c \right)=a\times b-a\times c\].

The distributive property of multiplication can be expressed under addition and subtraction. We can use distributive properties of addition and subtraction to rewrite expressions for different purposes.


Division of Integers

We learnt how to divide integers, both positive and negative. The following are the examples :

(a) Dividing a positive integer by a negative integer results in a negative integer as the quotient and vice-versa. For example, \[-24\div 3=-8\].

(b) Dividing a negative integer by another negative integer or dividing a positive integer by another positive integer results in a positive integer as the quotient. For example, $-35\div -5=7$ and $121\div 11=11$.


Properties of Division of Integers

Division of integers does not follow the commutative and associative properties.

For any integer $a$, 

(a) $a\div 0$ is not defined

(b) $0\div a=0,a\ne 0$

(c) $a\div 1=a$

(d) $a\div (-1)=-a$


Class 7 Integers Notes

In integers, we come across the negative set of values of whole numbers and also how they are represented on the number line. Integers introduce us to the property of negative numbers and extend the horizon of the definition of number line beyond natural number and whole number. The various properties that we come across in integers such as addition, subtraction, multiplication, and division of the integers are also useful in higher grades to understand the number system and newly introduced numbers in higher grades such as rational numbers, an irrational number, etc. Thus, keeping this thing in mind Vedantu has designed Class 7 Integers notes in a manner that helps the students in quick revision before they start with the chapters introduced in the higher grade. Thus, Vedantu has prepared revision notes for Integers chapter 1 so that students can easily revise the concepts before the exams as well as in future grades.


Benefits of Studying Class 7 Maths Chapter 1 Integers Revision Notes

  • Revision notes on Integers Class 7 are designed in such a way that students will be able to go through all the concepts at once in very little time.

  • Revision notes will benefit the students in various ways particularly it is going to speed up the problem-solving skills of the students and for this, we suggest practising these solutions regularly.

  • The revision notes provided by Vedantu are in a very illustrative and descriptive way. We keep every important point in their mind while preparing for a book like your exam pattern, important concepts which need to be highlighted again and again, etc.

  • With Class 7 Maths Chapter 1 Integers notes, Students will be able to learn and revise all the formulas even a moment before any exam and this last moment revision will be very beneficial also because it will accelerate their exam preparation.

  • The expert team of Vedantu would suggest students build the habit of revising Class 7 Maths notes Chapter 1 always before they start with problem-solving. The revision notes are designed keeping in mind the students' need for last-minute revision before the examination so they can optimize their results.

  • Before any test or exam, you will not require to turn all the pages of the chapter in a book to memorize the concepts or formulas, or properties of this chapter. Revision notes will solve this problem and you will not miss any important points at the end.

  • Putting and having all the required studs related to one chapter is very time-consuming but important as well and these revision notes help you to save that time which you can devote actually to practice which is more important to grab and master the concepts.


Tips for the studying Class 7 Maths Chapter 1 Notes

  • Go through each and every point relating it to the solved examples provided.

  • Prefer revising it every time you start solving the problems of the chapters.

  • Revise it again in future grades before you start with other chapters of the number system in higher grades i.e. Rational numbers, irrational numbers, etc.

  • Properly revise all the properties of operations on integers.


Chapter wise Revision Notes for Class 7 Maths


Summary

The basic concepts of natural numbers, whole numbers, operations of integers, and their properties are covered in CBSE Class 7 Maths Chapter 1 Integers notes. Students will have to get a clear idea of the fundamental concepts of this chapter to solve the sums. With practice, they will be able to identify the properties of addition, subtraction, multiplication, and division required in solving the sums from this chapter in the exam. Also, they should learn and practise the concept of the number line as it has applications in many other chapters. They can download the revision notes PDF prepared by our experts from our website and mobile app for free to prepare for their exam. 


Conclusion:

To sum up, we can conclude that revision notes of any chapter for Class 7 Mathematics literally help in learning the concepts or while practising or before the exams for revision. Vedantu has prepared its revision notes with an objective of an overall evolution of student’s concepts in a manner that the students understand all the theorems, formulas, and derivations or properties etc. in a way that will increase their subject knowledge and quite effectively by linking them with their practical applications. Solving the questions after referring to the Class 7 Integers notes for revision provided free of cost on our website will help the students to master the concepts and to score high marks.

FAQs on Integers Class 7 Notes CBSE Maths Chapter 1 (Free PDF Download)

1. How Class 7 Maths Ch 1 Notes are Helpful?

Integers Class 7 notes which are prepared by Vedantu are very helpful for 7th standard students as Vedantu provides you revision notes chapter-wise as each chapter needs extra effort and focus. These notes will help us to cover the various properties in the chapter Integers such as addition, subtraction, multiplication, and division of the integers which are also useful in higher grade to understand the number system and newly introduced numbers in higher grades such as rational number, an irrational number, etc. Talking about the maths subject of Class 7th it is totally a numerical-based or calculative subject and each chapter needs to be given proper time and needs to be revised again and again which can be done with these revision notes.

2. What all Things Class 7th Maths Chapter 1 Notes Contain?

In revision notes of Chapter 1, all important concepts with their formulas are highlighted so that you can grasp them easily. In chapter 1, we come across the negative set of values of whole numbers and also how they are represented on the number line and various properties such as addition, subtraction, multiplication, etc. These notes cover all these concepts with examples in them. Revising the same notes again and again built your command in that particular subject. Revision is the best way to memorize concepts easily in a very simple way.

3. Where can I download the latest Class 7 Integers notes?

Revision Notes are those short, crisp, clear, and simple worded study materials that students usually use as a last-minute revision refuge. These notes are available to download all across the internet as good notes have been created by professionals related to the subjects. But, Vedantu undoubtedly beats every one of them as they provide CBSE revision notes created through expert guidance, which incorporates shortcuts, tips, and techniques of Chapter 1 all of which are easily accessible CBSE Class 7 Maths Revision Notes Chapter 1. 

4. Can I download the Notes for Class 7 Integers in PDF?

PDFs for Notes of Chapter 1 of Maths for Class 7 are available to download over the internet. The only confusion is in determining where to download the best and most useful material. Notes are really useful to students in their exam preparation as they provide a one-stop destination to cover important topics during preparations and even right before the exams. One of the best and expert-provided revision notes is that of Vedantu which can be downloaded through this CBSE Class 7 Maths Revision Notes Chapter 1 or from the Vedantu app at free of cost.

5. How are the Notes beneficial for class 7 students for learning the chapter Integers?

Revision Notes are actually beneficial to students in more ways than they are aware of. The PDF format is the first advantage because of its easy portability and accessibility. Besides doing the job of providing comfort and easing the students’ minds with the knowledge that they have covered everything that they should from the chapter of Integers, they help students with their revisions and re-learning of all important concepts assuring them of getting one of the highest marks among their peers.

6. What are the basics in chapter 1 of Class 7 Maths?

CBSE Notes for Chapter 1 of Class 7 Maths offer students the option of being confident about covering all the important topics from the chapter. These notes offer well-prepared and precise information intended especially for students’ exams and thus, every important topic is covered with adequate attention.

  • The Properties of Integers which come under Addition, Subtraction, Multiplication, and Division

  • The Number Line

  • Introduction to the concept of Zero and its properties

These topics cover every important area in the chapter.

7. What are the important concepts to be remembered in chapter 1 of Class 7 Maths?

Class 7 Maths introduces the concepts of Integers to the students. CBSE Revision Notes address all the concepts in a way that guides and explains to students about every concept taught in the chapter in a simple and fun manner. The most important concepts from the chapter would undoubtedly be the number line and the different properties of Integers. The notes make it easier for students to remember these concepts due to the simple structure with which they have been prepared.