Addition of Integers


 
 
Concept Explanation
 

Addition of Integers

Addition of integers:

  • When two positive integers are added we get a positive integers. For example: 5+7 = 12
  • When two negative integers are added we get a negative integers. For example: (-3)+(-2) = (-5)
  • Example: Add  - 9005,   360

    Solution: - 9005 + 360 = - 8645

    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.

    Here the answer will be negative as 9005 is greater than 360 and sign of 9005 is negative.

    We now study the properties satisfied by addition:

  • Closure Property: Integers are closed for addition. That is, a+b ,where a and b are any integers.
  • Example: 2 + 3 = 5, whjere 2, 3 and 5 are integers.

    Example: (-3) + (-2) = (-5). where -2, - 3 and - 5 are integers.

  • Commutative Property: Two integers can be added in any order. In other words, addition is commutative for integers. If two integers a and b, then a+b = b+a for all integers.
  • Example: Verify the commutative property of addition for +16, -2

    RHS = +16 + (-2) = +16 - 2 = +14  and   LHS = -2 + 16 = +14

    Hence Verified 

  • Associative Property: Addition is associative for integers. In general, for any integers a, b and c, we can say, a + (b + c) = (a + b) + c
  • Example: Verify the commutative property of addition for +10, +7 and - 5.

    RHS = (a + b) + c = (+10 + 7) -5 = (+17) - 5 = +17 - 5 = +12

    LHS = a + (b + c) = +10 + (+7 - 5) = +10 + (+2) = +10 + 2 = +12

    Hence Verified

  • Additive Identity: when we add zero to any integer, the integers is remain same. Integer 0 is the identity under addition. That is,a + 0 = 0 + a = a for every integers a.
  • Example: Verify +9 for additive identity

    LHS = a + 0 = +9 + 0 = +9   and   RHS = 0 + a = 0 + (+9) = 0 + 9 = +9

    Hence Verified

    Sample Questions
    (More Questions for each concept available in Login)
    Question : 1

    Find the sum using the properties of addition:  ( - 40) + 100 + ( - 55)

    Right Option : A
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    Explanation
    Question : 2

    Add the following:  - 452 , 130

    Right Option : D
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    Explanation
    Question : 3

    Solve the following 

    (+48)+(-53)=

    Right Option : B
    View Explanation
    Explanation
     
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