Integers numbers are both positive numbers and negative numbers and which can be represented on the number line.
Properties of addition of integers:
1. The addition (sum) of any two integers is always an integer.
Example: -i) 3 + 8 = 11
ii) (- 3) + 8 = 5
iii) (- 3) + (- 8) = -11
iv) 3 + (- 8) = - 5 and so on.
2. For any two integers ‘a’ and ‘b’, a + b = b + a.
Example: -i) (+ 3) + (+ 7) = (+ 7) + (+ 3)
ii) (- 8) + (+ 4) = (+ 4) + (- 8)
iii)(- 6) + (- 5) = (- 5) + (- 6) and so on.
3. For any three integers ‘a’, ‘b’ and ‘c’. a + (b + c) = (a + b) + c
Example: -i) (- 3) + [(2) + (7)] = [(- 3) + (2)] + (7)
ii) 18 + [(- 5) + (- 12)] = [18 + (- 5) + (- 12)] and so on.
4. For any integer ‘a’, a + 0 = 0 + a = a
Example: -
i)(+ 5) + 0 = 0 + (+ 5) = + 5
ii) (- 13) + 0 = 0 + (- 13) = - 13 and so on.
5. The sum of an integer and its negative is always zero. i.e., a + (- a) = 0
Example: -i) 3 + (- 3) = 0
ii) (- 9) + 9 = 0 and so on.