Notes of chapter: Integers are presented below. Indepth notes along with worksheets and NCERT Solutions for Class 7.
(1)Integers = whole numbers and negative numbers
(2)Whole numbers =0, 1, 2, 3, 4,……….so on
(3)Negative number =-1, -2, -3, -4,………….so on
(4)Rules of operations (+, -, ×, ÷) for integers-
Rules for addition of integers –
(i) Addition of two positive integers gives a positive integer.
(+) + (+) = (+)
Eg: –
5+5=10
(ii) Addition of one positive and one negative integer gives either a positive integer or a negative integer. It depends upon the sign of bigger integer.
(+) + (-) = (-) or (+) [sign of bigger integer]
Eg :-
(a) (5) + (-6) = -1
(b) (8) + (-1)= 7
(iii) Addition of two negative integer gives a negative integer.
(-) + (-) = (-)
Eg :-
(-5)+ (-6) =-11
(iv) Additive inverse of a +ve integer is its –ve integer
Additive inverse of 4 is – 4
Additive inverse of -4 is 4
Rules for subtraction of integers-
(i) Subtraction of two integers gives either a positive integer or negative integer. It depends upon the sign of bigger integer.
Eg: –
(a) 7 – 5=12
(b) 5 – 7 = -2
(c) (5) – (-6) = 5 + 6 = 11
(d) (-5)- (-6) = -5 + 6 = 1
Rules for multiplication of integers-
(i) Multiplication of two positive integer gives a positive number.
(1) × (1) =1
Eg:-
5 × 5=25
(ii) Multiplication of one positive and one negative integer gives a negative integer.
(1) × (-1) =-1
Eg:-
5×-5=-25
(iii) Multiplication of two negative integers gives a positive integer.
(-1) × (-1) =1
Eg:-
(-2)× (-6) =12
(iv) Multiplication of three or more negative integers gives a positive integer if the number of negative integers is even. Multiplication of three or more negative integers gives a negative integer if the number of negative integers is odd.
(-1) × (-1) × (-1) =-1
(-1) × (-1) × (-1) × (-1) =1
Eg:-
(a)(-2)× (-4) × (-5)
= 8 ×-5
=- 40
(b) (-3)× (-4) ×2
=12×2
=24
Rules of division of integers-
(i) We divide a negative integer by a positive integer; we divide them as a whole numbers and then put a – sign before the quotient. We get a –ve integer.
-1÷1=-1
-20÷5=-4
(ii) We divide a positive integer by a negative integer, we divide them as a whole numbers and then put a – sign before the quotient. We get a –ve integer.
1÷ -1=-1
20÷-5=-4
(iii) We divide a positive integer by a positive integer, we divide them as a whole numbers and then put a + sign before the quotient. We get a +ve integer.
1÷1=1
20÷5=4
(iv) We divide a negative integer by a negative integer, we divide them as a whole numbers and then put a + sign before the quotient. We get a +ve integer.
-1÷ -1=1
-20÷-5=4
Helping Topics
Properties of Addition of Integers
Properties of Subtraction of Integers
Properties of Multiplication of Integers
Properties of Division of Integers