Dividing by any integer other than zero gives a certain result. which may not always be integers. But division by zero still stands at an undefined place.
If two different integers form the divisor and divisor, first determine the sign of the quotient according to their signs. If the numerator and divisor have the same sign, the quotient is positive. And if the numerator and divisor have opposite signs, the sign of the quotient is negative.
By practicing division of several integers, we can see-
i) Integer division is not closed. That is
When we divide two whole numbers we do not always get a whole number as a quotient.
ii) Division of two distinct integers does not obey the commutation rule. That is
If a and b are two distinct nonzero integers,
a ÷ b ≠ b ÷ a
iii) Division of integers does not follow the associative rule. That is
If a, b, c are three distinct non-zero integers,
a ÷ ( b ÷ c ) ≠ ( a ÷ b ) ÷ c
Although in the general case the division of three distinct integers does not obey the rule of association, if we take c = 1, we find that it obeys again. For example-
If a and b ( ≠ 0 ) are distinct integers,
a ÷ ( b ÷ 1 ) = ( a ÷ b ) ÷ 1
iv) Division of integers does not obey division rules. That is
If a, b, c are three distinct non-zero integers,
Although ( a + b ) ÷ c = a ÷ c + b ÷ c
a ÷ ( b + c ) ≠ a ÷ b + a ÷ c is.
A closer look reveals some more special events. As we have already learned, zero is an integer whose division is undefined.
But interestingly, if we divide zero by any non-zero integer, we always get zero. That is
If a is any nonzero integer,
0 ÷ a = 0
Again, 1 is an integer that, when divided by any other integer, never changes value. That is
If a is any integer,
a ÷ 1 = a
Again a similar phenomenon can be observed in case of (-1). In that case, even though the value of the integer remains the same, a change in sign can be observed. For example-
If a is any integer,
a ÷ (-1) = -a
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