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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