- Books Name
- CBSE Class 7 Mathematics Book
- Publication
- Param Publication
- Course
- CBSE Class 7
- Subject
- Mathmatics
Properties for Division of Integers
(i) Closure property of division of Integers : If ‘a’ and ‘b’ integers, then (a ÷ b) may not necessarily always be an integer ex. if a = –5 and b = 10 then
which is not an integer.
(ii) Commutative property for division of two integers : For any two integers ‘a’ and ‘b’ the commutative property does not hold true. i.e. a ÷ b ≠ b ÷ a. For example if a = 2 and b = –4 then 2 ÷ (–4)≠(–4) ÷ 2.
(iii) Associative Property for division : The associative property does not hold true for division of integers.
(v) For every integer a, a ÷ 1 = a. For example, if a = –10 then –10 ÷ 1 = –10.
(vi) For every integer a, we have a ÷ 0 is not defined.
(vii) For three non zero integers a, b and c, if a > b, then a ¸ c > b ÷ c if c is positive and a÷ c < b ÷ c if c is negative.
For example : Consider three integers a = 30 b = –20 and c = 10. where a > b
then a ÷ c = 30 ÷ 10 = 3 which is greater than
b ÷ c = 20 ÷ 10 = –2
But when c = –10 a ÷ c = 30 ÷ (–10) = –3 which is less than b ÷ c = –20 ÷ (–10) = 2