Properties of Adding Integers

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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