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Home >> Closure Property >> Division of Integers >>

Closure Property (Division of Integers)

Addition of Whole Numbers Addition of Integers Subtraction of Whole Numbers Subtraction of Integers Multiplication of Whole Numbers
Multiplication of Integers Division of Whole Numbers Division of Integers

Before you understand this topic you must know: What is Division of Integers

Explanation :- 
System of integers is not closed under division, this means that the division of any two integers is not always an integers. This is known as Closure Property for Division of Whole Numbers. 

Read the following and you can further understand this property:

(-6) ÷ 2 = (-3), Result is an Integer.......(1) 
(-27) ÷ (-9) = 3, Result is an Integer.....(2) 
15 ÷ (-5) = (-3), Result is an Integer ....(3) 

4 ÷ (-12) = (-1/3), Result is not an Integer, while it’s a fraction.....(4) 
(-6) ÷ 24 = (-1/4), Result is not an Integer, while it’s a fraction....(5) 
(-10) ÷ (-100) = (1/10), Result is not an Integer, while it’s a fraction....(6) 

From the above terms (1), (2) and (3), we notice that the division of integers is also an integer.

But also from the above terms (4), (5) and (6), we notice that the division of integers is not an integer (its Fraction). 

Hence, it can be concluded that division of two integers is not always an integer.


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Study More Solved Questions / Examples

  • Explain closure property of division of integers with the help of following positive integers:
    246 divided by 3
    5 divided by 25
  • Explain closure property of division of integers with the help of following negative integers:
    (-100) divided by (-5)
    (-7) divided by (-49)
  • Explain closure property of division of integers with the help of following equation:
    Equation 1 : (-36) ÷ (-12) =
    Equation 2 : (-46) ÷ (10) =
    Equation 3 : (105) ÷ (-5) =
    Equation 4 : (18) ÷ (33) =
  • Solve and following given two tables and on the basis of results, give your observation.

    Table – 1
    28÷(-14) =  
    (-72)÷(-9) =  
    81÷3 =  
    (-35)÷7 =  
    Table – 2
    (-27)÷(-18) =  
    35÷45 =  
    (-77)÷55 =  
    10÷(-14) =  

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