How To Do Long Division With Positive & Negative Integers

Long division refers to dividing numbers by hand. Whether the numbers are long or small, the method is the same, even if longer numbers seem a little more intimidating. Performing long division in integers simply means the numbers are whole numbers without fractions or decimals. A special case lies with negative numbers, but it doesn't change the procedure, only the final sign. If only one of the two numbers is negative, the resulting calculation will also be negative. If both numbers are negative, the resulting calculation will be positive, since the two negative signs cancel out each other.

Step 1

Take note of the signs of the two numbers. If both signs are positive or both are negative, the resulting figure will be positive. If only one of the signs is negative, you will end up with a negative number. As an example, 78 divided by -5 would give you a negative quotient.

Step 2

Set up the calculation by writing the dividend, or the number being divided into, with a division bracket over it. The divisor will go on the left. In the example, you would draw out:

-5/78

You can safely ignore the negative sign, as long as you remember the final outcome will be negative.

Step 3

Divide the first digit of the dividend by the divisor. If the first digit is smaller than the divisor, divide the divisor into the first two digits. Record the number of times the divisor evenly goes into the dividend digit(s) on the top, with the remainder written below. In the example, "1" would be written on top directly over the "7," and the remainder of "2" would be written under the "7."

Step 4

Drop the next digit down next to the remainder. In the example, you would then have "28" with the two aligned under the "7."

Step 5

Repeat the division into this new number. Record the whole number to the right of the preceding whole number at the top and write the remainder under the last digit you brought down. In the example, you would write "5" right after "1" and write "3" under the "8."

Step 6

Repeat until you have a whole number written directly over the last digit of the dividend. In the example, you would pause at 15. Now you have a few choices. You can write the equation as "25 with a remainder of 3," or you could express it as a fraction by placing the remainder over the divisor, such that it looks like "25 3/5," or you can place a period after the "25" and continue until you have no remainder (or find a remainder that keeps repeating). In the example, the latter option would result in "25.6."

Step 7

Add the negative sign, if required from your initial determination. In the example, the result requires a negative sign, so the result would be one of the following:

-25 with a remainder of 3 -25 3/5 -25.6