The properties of subtracting integers are explained here
along with the examples.1. Closure Property: The difference (subtraction) of any two integers is always an integer.i.e., The difference of two integers is always an integer.Hence, integers are closed under subtraction. If x and y are any two integers, then x – y always an integerFor Examples:(i) (+7) – (+4) = 7 – 4 = 3, which is an integer.(ii) (-8) – (+3) = -8 – 3 = -11, which is an integer. (iii) 6 – 14 = 6 + (-14) = – 8, which is an integer.(iv) (- 18) – 10 = (- 18) + (- 10) = – 28, which is an integer.
2. Commutative Property: Subtraction is not commutative for integers.For any two different integers ‘x’ and ‘y’,x – y ≠ y – xFor Examples:(i) 4 – 8 = 4 + (-8) = -4 and 8 – 4 = 8 + (- 4) = 4Therefore, 4 – 8 ≠ 8 – 4(ii) (- 4) – 7 = (- 4) + (- 7) = – 11 and 7 – (-4) = 7 + 4 = 11Therefore, (- 4) – 7 ≠ 7 – (-4)3. Associative Property: Subtraction is not associative for integers.For any three integers ‘x’, ‘y’ and ‘z’, x – (y – z) ≠ (x – y) – zFor Example:[2 – (- 3)] – (- 6) = [2 + (3)] + 6 = 5 + 6 = 11 and2 – [(- 3) – (- 6)] = 2 – [(- 3) + 6] = 2 – 3 = -1Therefore, [2 – (- 3)] – (- 6) ≠ 2 – [(- 3) – (- 6)]4. Subtraction Property of Zero: The result of subtracting zero from an integer is the integer itself.For any three integers ‘x’,x – 0 = xFor Example:(i) 5 – 0 = 5(ii) 8 – 0 = 8(iii) 100 – 0 = 100(iv) 9999 – 0 = 9999(v) 99999999 – 0 = 999999995. For any integer ‘x’, x – 0 ≠ 0 – xFor Example:(i) 7 – 0 = 7 and 0 – 7 = -7Therefore, 7 – 0 ≠ 0 – 7(ii) 10 – 0 = 10 and 0 – 10 = -10 Therefore, 10 – 0 ≠ 0 – 106. For any three integers ‘x’, ‘y’ and ‘z’, and x > y, thenx – z > y – zTo 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]= – 22. Evaluate the expression (-45) +
(-32) – (-69) + (87)Solution: (-45) + (-32) – (-69) + (87)= -45 – 32 + 69 +87Add all the positive terms and add
all the negative terms= -(45 + 32) + (69 + 87)= -77 + 156= +79= 793. Simplify: 32 – 13 + 35 + 18 –
60Solution:32 – 13 + 35 + 18 – 60Add 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= -10Therefore the other number is -10.
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