Class 7 Maths Integers – Get here the Notes, Question & Practice Paper of Class 7 Maths for topic Integers Notes. Integers Notes for Class 7 Maths are here. You can download the Integers Notes PDF to study all the topics in this chapter. Moreover the Class 7 Maths notes include chapter summary, definitions, examples, and key pointers for Integers. Thus if you are studying class Maths (गणित), then the Integers notes will help you easily understand the topic and ace it.
Class 7 Maths Notes for Integers
Integers is a critical part in the study of Maths. In India, it is taught in class. Therefore the Class 7 Notes for Maths topic Integers have been compiled by teachers and field experts. They explain the complete chapter of Integers in one-shot.
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Integers Notes for Class 7 Maths
Integers Class 7 notes is as follows. You can view the document here and also download it use it anytime for future reference whenever you want to brush up your concepts of Maths.
Chapter 1 – Integers
Previous Knowledge:
Integers – Integers are bigger collection of numbers which is formed by whole numbers and their negatives or we can say that all positive and negative numbers including zero are integers.
Example: -3, -2, -1, 0, 1, 2, 3…
Integers on Number Line – On a number line, when we:
- add a positive integer, we move to the right.
- add a negative integer, we move to the left.
- subtract a positive integer, we move to the left.
- subtract a negative integer, we move to the right.
Properties of Addition and Subtraction of Integers
(a) Closure Property: Integers are closed for addition and subtraction both, i.e. a + b and a – b are again integers, where a and b are any integers.
Example: For any two integers 2 and 3, we have 2+ 3 = 5 an integer and 2 – 3 = -1 is also an integer.
(b) Commutative Property: Addition is commutative for integers, i.e. a + b = b + a for all integers a and b.
Example: For any two integers say 5 and 4, we have 5+ 4 = 4 + 5 = 9, but the same does not holds for subtraction as 5– 4 =1 and 4 – 5 = -1.
(c) Associative Property: Addition is associative for integers, i.e., (a + b) + c = a + (b + c) for all integers a, b and c.
Example: For any three integers say 6, 3 & 7 we have (6 + 3) +7= 6 + (3 + 7) Again it does not hold under subtraction.
(d) Additive Identity: Integer 0 is the identity under addition i.e. a + 0 = 0 + a = a for every integer a.
Example: 3 + 0 = 0 + 3 = 3
Multiplication of Integers
The product of a positive and a negative integer is a negative integer, whereas the product of two negative integers is a positive integer and the product of two positive integers is always a positive integer.
Example: – 2 × 7 = – 14 and – 3 × – 8 = 24 and 5 × 6 = 30.
Also we can see that the product of even number of negative integers is positive. whereas the product of odd number of negative integers is negative.
Example: (-1) × (-1) × (-1) × (-1) = 1 but (-1) × (-1) × (-1) = -1.
Properties of Multiplication of Integers
(a) Closure Property: Integers are closed under multiplication, i.e., a × b is an integer for any two integers a and b,
Example: 2 x 3 =6, 6 is also an integer.
(b) Commutative Property: Multiplication is commutative for integers, i.e., a × b = b × a for any integers a and b
Example: 4 x 3 = 3 x 4 = 12.
(c) Associative Property: Multiplication is associative for integers, i.e., (a × b) × c = a × (b × c) for any three integers a, b & c.
Example: (2 × 3) × 4 = 2 × (3 × 4) = 24
(d) Multiplicative Identity: The integer 1 is the identity under multiplication, i.e., 1 × a = a × 1 = a for any integer a.
Example: 1 × 9 = 9 × 1 = 9
(e) Distributive Property: Under addition and multiplication, integers show a property called distributive property i.e., a × (b + c) = (a × b) + (a × c) for any three integers a, b and c.
Examples:
i) 16 x12 = 16 x (10 +2) = (16 x 10) + (16 x 2) = 160 + 32 =192
ii) -23 x 48 = -23 x (50 – 2) = (-23 x 50) + (-23 x 2) = -1150 + (-46)
= -1150 – 46 = -1196
iii) 52 x (-8) + (-52) x 2 = [52 x (-8)] + [ 52 x (-2)] = 52 x [(-8 -2)] =52 x (-10) = -520.
Properties of Division of Integers
(a) When a positive integer is divided by a negative integer, the quotient obtained is a negative integer and vice-versa.
Example: 2/−3 = – 2/3
(b) Division of a negative integer by another negative integer gives a positive integer as quotient.
Example: −5 / −6 = 5 / 6
Other Properties of Integer: For any integer a, we have (i) a ÷ 0 is not defined and (ii) a ÷ 1 = a. Example: 4÷0 is not defined and 6 ÷1 = 6
Candidates who are ambitious to qualify the Class 7 with good score can check this article for Notes, Study Material, Practice Paper. Above we provided the link to access the Notes, Important Question and Practice Paper of Class 7 Maths for topic Integers.
All Topics Class 7 Maths Notes
Chapter wise notes for Maths (गणित) are given below.
- Integers
- Fractions and Decimals
- Data Handling
- Simple Equations
- Lines & Angles
- Triangles & Its Properties
- Comparing Quantities
- Rational Numbers
- Perimeter and Area
- Algebraic Expressions
- Exponents and Powers
- Symmetry
- Visualing Solid Shapes
Class 7 Notes for All Subjects
NCERT Solutions for Class 7 Maths Integers
The Integers notes here help you solve the questions and answers. Also, you can complete the Class 7 Integers worksheet using the same. In addition you will also tackle CBSE Class 7 Maths Important Questions with these Class 7 notes.
However if you still need help, then you can use the NCERT Solutions for Class 7 Maths Integers to get all the answers. Integers solutions contain questions, answers, and steps to solve all questions.
Notes for All Classes
- Class 6 Notes
- Class 7 Notes
- Class 8 Notes
- Class 9 Notes
- Class 10 Notes
- Class 11 Notes
- Class 12 Notes
Integers Notes for Class 7 Maths – An Overview
| Name of Topic | Integers |
| Class | 7 |
| Subject | Maths |
| All Class 7 Maths Notes | Class 7 Maths Notes |
| All Class 7 Notes | Class 7 Notes |
Class 7 Integers Notes for All Boards
You can use the Class 7 Maths notes of Integers for all boards.
The education boards in India for which Integers notes are relevant are – CBSE, CISCE, AHSEC, CHSE Odisha, CGBSE, HBSE, HPBOSE, PUE Karnataka, MSBSHSE, PSEB, RBSE, TBSE, UPMSP, UBSE, BIEAP, BSEB, GBSHSE, GSEB, JAC, JKBOSE, KBPE, MBOSE, MBSE, MPBSE, NBSE, DGE TN, TSBIE, COHSEM, WBCHSE.
Therefore you can refer to these notes as CBSE, CISCE, AHSEC, CHSE Odisha, CGBSE, HBSE, HPBOSE, PUE Karnataka, MSBSHSE, PSEB, RBSE, TBSE, UPMSP, UBSE, BIEAP, BSEB, GBSHSE, GSEB, JAC, JKBOSE, KBPE, MBOSE, MBSE, MPBSE, NBSE, DGE TN, TSBIE, COHSEM, WBCHSE notes for class Class 7 / Class / Maths for the topic Integers.
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