Class 7 Chapter 1 Maths Integers Notes (NCERT)

Class 7 Chapter 1 Maths Integers Notes (NCERT) to make the chapter easier. I hope it helps you.

1. 1)




2) Properties of integers->
a. Closure->
i. Addition->Yes; int+int=int
ii. Subtraction->Yes;int-int=int
iii. Multiplication->Yes;int×int=int
iv. Division->No;For eg->3÷7=
3
7
(Not an integer)
b. Commutative->
i. Addition->Yes;a+b=b+a
ii. Subtraction->No;For eg:3-7≠7-3
iii. Multiplication->Yes;ab=ba
iv. Division->No;For eg->3÷7≠7÷3
c. Associative->
i. Addition->Yes;a+(b+c)=(a+b)+c
ii. Subtraction->No;For eg->3-(-7-2)≠(3-7)-2
iii. Multiplication->Yes;ab×c=a×bc
iv. Division->No;For eg->(3÷7) ÷-2≠3÷(7÷-2)
d. Distributivity under Multiplication->
i. Addition->Yes;a(b+c)=ab+ac
ii. Subtraction->Yes;a(b-c)=ab-ac
3) -a×-a………...×-a=positive integer;-a×-b=a×b


Natural
Numbers(1,2..........∞)
Whole
Numbers(0,1.......∞)
Integers(-∞..........-2,-
1, 0, 1, 2........... ∞)
1,2……………………..∞
0
-∞……………………-2,-1

Even times

2. 4) -a×-a………...×-a=negative integer;a×-b=-(a×b)

5) -a÷-a………...÷-a=negative integer;a÷-b=-(a÷b) (where
b,a≠0)

6) -a÷-a…………÷-a=positive integer;-a÷-b=a÷b(where
b,a≠0)
7) Other properties->
a. a×0=0
b. a×1=a(1=multiplicative identity)
c. a+0=a(0=additive identity)
d. a-0=a
e. a÷1=a
f. a÷0=not defined





Odd times
Odd times
Even times