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
Add all the positive terms and add all the negative terms
= (45 + 32) + (69 + 87)
= 77 + 156
= +79
= 79
3. Simplify: 32 – 13 + 35 + 18  60
Solution:
32 – 13 + 35 + 18 – 60
Add all the positive terms and add all the negative terms
= (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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