The properties of dividing integers are discussed here along with the examples.
1. If ‘a’ and ‘b’ are any two integers, then ‘a’ ÷ ‘b’ is not necessarily an integer.
For example:
(i) +12/+3 = +4, which is an integer.
(ii) +45/15 = 3 which is an integer.
(iii) 135/+9 = 15 which is an integer.
(iv) 725/25 = + 29 which is an integer.
But,
(v) (+7)/(+4) is not an integer and same is true for (5) ÷ (+2), (+15) ÷ (7), (10) ÷ (3), etc.
2. If ‘a’ is not negative integer i.e., a ≠ 0; then ‘a ÷ a’
is always equal to unity (1).
For example:
(i) (3) ÷ (3) = (+1) = 1
(ii) (+9) ÷ (+9) = (+1) = 1
(iii) (+17) ÷ (+17) = (+1) = 1
(iv) (25) ÷ (25) = (+1) = 1 and so on.
3. For any nonzero integer ‘a’, 0 ÷ a = 0, but a ÷ 0 is not defined.
When zero (0) is divided by any nonzero number, the result (quotient) is always zero and when any number is divided by zero (0), the result is notdefined.
i.e., Zero/Any nonzero number = Zero and Any number/Zero = Notdefined
For example:
(i) 0/12 = 0, 0/(15) = 0, 0/123 = 0 and so on.
(ii) 15/0 = notdefined, 18/0 = notdefined, 0/0 = notdefined.
Similarly, 0 ÷ 7 = 0, 0 ÷ (10) = 0, but 12 ÷ 0 is not defined and so is (15) ÷ 0 and so on.
Also, a ÷ b ≠ b ÷ a
For example:
4 ÷ 2 ≠ 2 ÷ 4
a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c
For example:
8 ÷ (4 ÷ 2) ≠ (8 ÷ 4) ÷ 2 and so on.
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