Integer Division

Now that you’ve learned how to multiply integers, dividing integers should be a breeze. The reason is that they follow the same rules.

Rules on How to Divide Integers

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.

Examples of Integer Divisions

Example 1: Divide the two integers below.

find the quotient of negative 56 and negative 7 that is -5/(-7)

Solution: First, find the absolute values of the two integers.

the absolute value of negative 56 is equal to positive 56 while the absolute value of negative 7 is positive 7.

Next, divide the numbers or find their quotient.

the quotient of positive 56 and positive 7 is positive 8 which can also be written as 56/7=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.

-56/(-7)=+8

Example 2: Divide the two integers below.

positive 24 divided by negative 8 which can also be written numerically as +24/(-8)

Solution: Divide the absolute values of the two integers.

the quotient of the absolute value of +24 and the absolute value of -8 is +3

Following the rules stated above, when dividing integers with different signs the final answer (quotient) is negative.

positive 24 divided by negative 8 equals negative 3, which can also be written as +24/(-8)=-3

Example 3: Divide the three integers below from left to right

this integer division problem requires a multi-step solution: negative 252 divided by positive 7 divided by negative 9, which can also be written as -252/(+7)/(-9)

Solution: To divide three or more integers, it is important that we perform the division operation from left to right. In addition, we can accomplish it by dividing two integers at a time. The parenthesis shows the first two integers to divide, and whatever is the result or quotient will be divided by the next one. So we have here,  252 divided by 7 is equal to – 36. It is a negative quotient since we are dividing two integers that have different signs. Then we take that quotient and divide it by the integer that follows. We get 36  ÷ 9 = 4.

-252/(+7)/(-9)=[(-252)/(+7)]/-9=(-36)/-9=+4

Practice with Worksheets

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