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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