Method

Dividing Integers With Different Signs

The quotient of dividing two integers is always negative if and only if one is negative and the other is positive. Change the negative number to its opposite and perform the division as if they were whole numbers. Next, change the result to its opposite to get the quotient of the initial division. This process will be illustrated with the following division. -12÷4 There are three steps to follow to find the quotient when dividing two numbers with different signs.

Check the Signs of the Integers

Identify which of the numbers involved in the division is negative. Next, change it to its opposite to get a division of two positive integers. In the given example, the dividend -12 is negative. Its opposite is 12. -12÷4 ⇒ 12÷4

Find the Quotient of the Resulting Division

Find the quotient of the division of two whole numbers. For this example, 12÷4 means how many jumps of 4 are needed to reach 12 on a number line, starting from zero.

It took three jumps of 4 units to reach 12. This means that 12÷4=3.

Change the Quotient to Its Opposite

Change the quotient found in the previous step to its opposite to get the quotient of the initial division of integers with different sings. For the given example, the quotient is 3. Its opposite is -3. Therefore, the quotient of - 12 ÷ 4 is - 3. 12÷4= 3 ⇒ -12÷4= -3 In summary, divide two integers with different signs as if they were whole numbers and change the result to its opposite to get the final quotient.

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