CBSE Class 8 - Mathematics - Chapter 1 - Integers (Key Points) (#cbsenotes)(#eduvictors)

Mathematics - Chapter 1 - Integers
(Key Points)

⑴ Integers are a bigger collection of numbers which is formed by whole numbers and their negatives.

⑵You have studied in the earlier class,  about the representation of integers on the number line and their addition and subtraction.

⑶ We now study the properties satisfied by addition and subtraction.
(a) Integers are closed for addition and subtraction both. That is, a + b and a – b are again integers, where a and b are any integers.

(b) Addition is commutative for integers, i.e., a + b = b + a for all integers a and b.

(c) Addition is associative for integers, i.e., (a + b) + c = a + (b + c) for all integers a, b and c.

(d) Integer 0 is the identity under addition. That is, a + 0 = 0 + a = a  for every integer a.

⑷We studied, how integers could be multiplied and found that product of a  positive and a negative integer is a negative integer, whereas the product of two negative integers is a positive integer. For example, – 2 × 7 = – 14 and – 3 × – 8 = 24.

⑸ Product of even number of negative integers is positive, whereas the product of an odd number of negative integers is negative.



⑹ Integers show some properties under multiplication.

(a) Integers are closed under multiplication.  That is,  a  ×  b  is an integer for any two integers a and b.

(b) Multiplication is commutative for integers. That is, a × b = b × a for any integers a and b.

(c) The  integer  1  is  the  identity  under  multiplication,  i.e.,  1  ×  a  =  a  ×  1  =  a  for  any
integer a.

(d) Multiplication is associative for integers, i.e., (a × b) × c = a × (b × c) for any three integers a, b and c.

⑺Under addition and multiplication, integers show a  property called distributive property. That is, a × (b + c) = a × b + a × c for any three integers a, b and c.

⑻ The properties of commutativity, associativity under addition and multiplication, and the distributive property help us to make our calculations easier.

⑼ We also learnt how to divide integers. We found that,

(a) When a positive integer is divided by a negative integer, the quotient obtained is a negative integer and vice-versa.

(b) Division of a negative integer by another negative integer gives a positive integer as a quotient.


⑽ For any integer a, we have the distributive property help us to make our calculations easier.


⑾ We also learnt how to divide integers. We found that,

(a) When a positive integer is divided by a negative integer, the quotient obtained is a negative integer and vice-versa.

(b) Division of a negative integer by another negative integer gives a positive integer as a quotient.

⑿ For any integer a, we have
 a ÷  0 = not defined
 a ÷  1 = a


☛See also:
Ch 1 - Integers (NCERT Ex 1.2)
Ch 1 - Integers (NCERT Ex 1.3)
Ch 1 - Integers (Key Points)

Ch 2 - Decimals - Multiplication and Division (Worksheet)
Ch 2 - Fractions and Decimals - NCERT Exercise Answers 2.6

Ch 3 - Data Handling (NCERT Ex 3.4)

CH 4 - Simple Equations (NCERT Ex 4.4)
CH 4 - Simple Equations (Worksheet)

CH6 - Lines and Angles (Worksheet)

CH8 - Comparing Quantities (Ratio and NCERT Ex 8.1)
CH8 - Comparing Quantities (Percentage and NCERT Ex 8.2) 
CH8 - Comparing Quantities(NCERT Ex 8.3)

Chapter 12 - Algebraic Expressions (Revision Sheet)
Chapter 12 - Algebraic Expressions - NCERT Solution 12.1
Chapter 12 - Algebraic Expressions (Worksheet)

Chapter 13: Exponents and Powers (MCQs)