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Maths / Integers / Subtraction Of Integers
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Subtraction Of Integers

Subtraction of Integers: To subtract integers like a and b, then to subtract b from a, we change the sign of b and add it to a: a – b = a + (-b)

Example: Subtract 3 from -8

Solution: As we have to subtract 3 from -8, we change the sign of 3 and add it to -8. Thus, we have -8 -3 = (-8) + (-3) = -11 . To add two negative integers, first add the absolute value i.e. 8 + 3 = 11, then place the negative sign as both integers are negative. Final answer = -11

Example: Subtract -10 and -11

Solution : -10 - (-11) . Here, the two minus symbol will become plus. So, we get -10 + 11 = +1

If the signs are different subtract the smaller absolute value from the larger absolute value. The sign will be the sign of the integer that produced the larger absolute value.

Example: Simplify: 14 - (+6)

Solution: 14 - (+6) = 14 - 6 = 8. The answer if positive because sign will be used of larger absolute integer which is 14 and it is positive.

Properties satisfied by subtraction:

  • Closure Property: When we subtract two integers, we get an integer. Hence integers are closed for subtraction. That is a-b, where a and b are any integers.
  • Example: Verify closure property under subtraction: Subtract -9 from 8:

    Solution: 8 - (-9) : Two negative symbols will become plus. 8 + 9 = +17 which is an integer.

  • Commutative Property: Subtraction is not commutative for integers. for integers a and b: large a-bneq b-a.
  • Example: Verify commutative property under subtraction for +5 and +2:

    Solution: Let a = +5 and b = +2

    RHS = b - a = +2 - (+5) = +2 - 5 = -3

    LHS = a - b = +5 - (+2) = +5 -2 = +3

    large LHSneq RHS. Hence verified.

  • Associative Property: In general, for any three integers a , b and c. (a-b)-cneq a-(b-c). Hence, integers do not follow associative property under subtraction.
  • Example: Verify Associative Property of integers (+9), (-3) and (+4)  

    Solution: Let a = +9 ,  b = -3 and c = +4

    LHS = (a - b) - c = (+9 - (-3)) - (+4) = (+9 + 3) - 4 = +12 - 4 = +8

    RHS = a - (b - c) = +9 - (-3 - (+4)) = +9 - (-3 - 4) = +9 - (-7) = +9 + 7 = +16

    large LHSneq RHS .  Hence Verified


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