# Properties of Subtracting Integers

The properties of subtracting integers are explained here along with the examples.

1. The difference (subtraction) of any two integers is always an integer.

Examples:

(a) (+7) – (+4) = 7 - 4 = 3, which is an integer.

(b) (-8) – (+3) = -8 – 3 = -11, which is an integer.

2. For any two different integers ‘a’ and ‘b’, a - b ≠ b - a

3. For any three integers ‘a’, ‘b’ and ‘c’, a - (b - c) ≠ (a - b) - c

4. For any integer ‘a’, a - 0 ≠ 0 - a

To evaluate an expression containing various integers with plus and minus sign:

1. Evaluate:

(i) (+15) + (-11) - (+5) - (-7)

= 15 - 11 - 5 + 7

= 22 – 16, [Adding all integers with plus (+) sign together and with minus (-) sign respectively together]

= +6 or simply 6.

(ii) (-72) + (-93) - (-85) + (+78)

= -72 -93 + 85 + 78

= -165 + 163, [Adding all integers with plus (+) sign together and with minus (-) sign respectively together]

= - 2

2. Evaluate the expression (-45) + (-32) – (-69) + (87)

Solution:

(-45) + (-32) – (-69) + (87)

= -45 – 32 + 69 +87

= -(45 + 32) + (69 + 87)

= -77 + 156

= +79

= 79

3. Simplify: 32 – 13 + 35 + 18 - 60

Solution:

32 – 13 + 35 + 18 – 60

= (32 + 35 + 18) – (13 + 60)

= 85 – 73

= +12 or simply 12

4. The sum of two integers is -17. If one of them is -7, find the other.

Solution:

Other integer = Sum of two integers - the given integer

= (-17) – (-7)

= -17 + 7

= -10

Therefore the other number is -10.

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