Dividing Integers

Dividing integers is the fourth operations on integers, among the four fundamental operations on integers and it is the process of finding how often one give number (called divisor) is contained in another given number (called dividend).

The number expressing the times the divisor is contained in the dividend is called the quotient.

The sign or symbol of division is ‘÷’ and it is read as divided by.

Thus, 32 ÷ 8 is 32 divided by 8.

Note: 32 ÷ 8 = 32/8 = 4; 45 ÷ 3 = 45/3 = 15, 91 ÷ 13 = 91/13 = 7 and so on.

63 ÷ 9 = 63/9 = 7 indicates that in 63, 9 is contained 7 times.

Therefore, 9 is divisor, 63 is dividend and 7 is quotient.

Similarly, 125 ÷ 5 = 125/5 = 25 indicates that in 125, 5 is contained 25 times.

Therefore, 5 is divisor, 125 is dividend and 25 is quotient.


The rules for division are the same as the rules for multiplication i.e.,

1. If both the integers have like signs (both positive or both negative), the sign of division (quotient) is always positive.

For example:

(i) (+8)/(+4) = +2

(ii) (-9)/(-3) = +3

(iii) (+84)/(+4) = +21

(iv) (-49)/(-7) = +7                            and so on.


2. If both integers have unlike signs, the division (quotient) is always negative.

For example:

(i) (+6)/(-3) = (-2)

(ii) (-8)/(+4) = -2

(iii) (-22)/(+11) = +2

(iv) (+32)/(-8) = - 4                            and so on.

Note: (-52)/4 = 52/(-4) = -(52/4) = -13

72/(-6) = - (72)/6 = (-72)/6 = -12                            and so on.


Solved example on dividing integers:

Divide the following integers:

(i) 96 by 12

= 96/12 = 8

(ii) 96 by -12

= 96/(-12) = -8

(iii) -96 by -12

= (-96)/(-12) = 8

(iv) -96 by 12

= (-96)/12 = -8

(v) 98 by 0

= not-defined

(vi) 98 by 0

= 0


Note:

Dividend

(+)

(+)

(-)

(-)


÷

÷

÷

÷

Divisor

(+)

(-)

(+)

(-)


=

=

=

=

Quotient

(+)

(-)

(-)

(+)






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