# Dividing Positive and Negative Integers

In the previous post on integers, we have learned the rules in multiplying positive integers and negative integers. In this post, we are going to learn how to divide positive and negative integers.

If you have observed, in the post on subtracting integers, we have converted the “minus sign” to a “plus negative sign.” I think it is safe for us to say that subtraction is some sort of “disguised addition.” Similarly, we can also convert a division expression to multiplication. For example, we can turn

$\displaystyle \frac{5}{3}$ to $(5 \times \frac{1}{3})$.

In general, the division

$\displaystyle \frac{a}{b}$ to $(a \times \frac{1}{b})$.

From the discussion above, we can ask the following question:

Can we use the rules in multiplying integers when dividing integers?

The answer is a big YES. The rules are very much related.

positive integer ÷  positive integer = positive integer
positive integer ÷  negative integer = negative integer
negative integer ÷  positive integer = negative integer
negative integer ÷  negative integer = positive integer

Notice that they are very similar to the rules in multiplying integers.

positive integer x  positive integer = positive integer
positive integer x  negative integer = negative integer
negative integer x  positive integer = negative integer
negative integer x  negative integer = positive integer

Here are some examples worked examples.

1. 18 ÷ 3 = 6

2.36 ÷ -12 = – 3

3. -15 ÷ 2 = – 7.5

4.- 8 ÷ -4 = 2

From the discussion and the worked examples above, we can therefore conclude that in dividing positive and negative integers, we only need to memorize the rules in multiplying integers and apply them in dividing integers.