The properties of adding integers are discussed here along with the examples.
1. The addition (sum) of any two integers is always an integer.
For example:
(i) 5 + 9 = 14 ∈ Z
(ii) (5) + 9 = 4 ∈ Z
(iii) (5) + (9) = 14 ∈ Z
(iv) 5 + (9) = 4 ∈ Z and so on.
2. For any two integers ‘a’ and ‘b’; a + b = b + a
For example:
(i) (+3) + (+8) = (+8) + (+3)
(ii) (7) + (+3) = (+3) + (7)
(iii) (9) + (3) = (3) + (9)
(iv) (+5) + (3) = (+5) + (3) and so on.
3. For any three integers ‘a’ ‘b’ and ‘c’; a + (b + c) = (a + b) + c
For example:
(i) (+5) + [(2) + (+3)] = [(+5) + (2)] + (+3)
(ii) (3) + [(4) + (5)] = [(3) + (4)] + (5)
(iii) (+4) + [(+2) + (+3)] = [(+4) + (+2)] + (+3)
(iv) (2) + [(+3) + (4)] = [(2) + (+3)] + (4)
(v) (4) + [(3) + (+5)] = [(4) + (3)] + (+5)
(vi) (+3) + [(+4) + (2)] = [(+3) + (+4)] + (2)
(vii) (3) + [(2) + (7)] = [(3) + (2)] + (7)
(viii) 9 + [(4) + (2)] = [9 + (4)] + (2) and so on.
4. For any integer ‘a’; a + 0 = 0 + a = a
For example:
(i) (+7) + 0 = 0 + (+7) = +7
(ii) (11) + 0 = 0 + (11) = 11
(iii) 0 + (+9) = (+9) + 0 = +9
(iv) 0 + (5) = (5) + 0 = 5 and so on.
5. Any integer + its negative = 0 i.e., a + (a) = 0
For example:
(i) 5 + (5) = 0
(ii) (7) + 7 = 0 and so on.
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