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.
Numbers Page
6th Grade Page
From Properties of Dividing Integers to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.