# Integers

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