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

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:

(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

• Chapter 2 - Fractions and Decimals Notes

• Chapter 3 - Data Handling Notes

• Chapter 4 - Simple Equations Notes

• Chapter 5 - Lines and Angles Notes

• Chapter 6 - The Triangle and Its Properties Notes

• Chapter 7 - Congruence of Triangles Notes

• Chapter 8 - Comparing Quantities Notes

• Chapter 9 - Rational Numbers Notes

• Chapter 10 - Practical Geometry Notes

• Chapter 11 - Perimeter and Area Notes

• Chapter 12 - Algebraic Expressions Notes

• Chapter 13 - Exponents and Powers Notes

• Chapter 14 - Symmetry Notes

• Chapter 15 - Visualising Solid Shapes Notes

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.