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Maths / Integers / Division of Integers
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Division of Integers

Rules on How to Divide Integers are:

  • Step 1: Divide their absolute values.
  • Step 2: Determine the sign of the final answer (known as a quotient) using the following conditions.
  • Condition 1: If the signs of the two numbers are the same, the quotient is always a positive number.

    • This illustration shows the rules of dividing integers with the same sign. For the first case, a positive integer divided by another positive integer is always positive. On the other hand, a negative integer divided by another negative integer is always positive. Simply put, the quotient of two integers with the same sign will always yield a positive integer solution.

  • Condition 2: If the signs of the two numbers are different, the quotient is always a negative number.

    • This diagram shows the rules that govern when we divide two integers with different signs. The first case implies that a positive integer divided by a negative integer results to an answer of an integer with a negative sign. Likewise, a negative integer divided by a positive integer outputs an integer with a negative sign as well. In summary, the quotient of two integers with different signs will always yield a negative integer solution.

    Example : Divide the two integers (-56) by (-7) :

    Solution: Divide the absolute values of the two integers 56div 7 = 8.  Finally, determine the final sign of the answer or quotient. Because we are dividing two integers with the same sign, the quotient will have a positive sign. -56div (-7) = 8

    Example : Divide the two integers (+24) by (-8)

    Solution: Divide the absolute values of the two integers 24div 8 = 3.  When dividing integers with different signs the final answer (quotient) is negative. 24div (-8) = -3

    For any integer a, we have

  • adiv 0 ;is; not; define
  • adiv 1=a
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