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Negative Divided by Positive or Positive Divided by Negative

Whether you are dividing a negative number by a positive number or dividing a positive number by a negative number, the quotient will be a negative number.

Negative Number Divided by a Positive Number

Positive Number Divided by a Negative Number

Let's do another example.

Step One: Determine the Signs

When we are dividing $14,$ which is positive, by $-7,$ which is negative, our quotient will be negative.

When we are dividing $-24,$ which is negative, by $4,$ which is positive, our quotient will be negative.

Step Two: Pretend the Numbers are Positive and Divide

$$14 \div 7 = 2$$ $$24 \div 4 = 6$$

Step Three: Solution!

$$\text{negative } 2 \text{ plus }\text{negative } 6 = (-2)+(-6) = -8$$

(Video) Dividing Integers

by mathman1024

Here is a video by mathman1024 that goes over dividing positive integers, dividing negative integers, and dividing a negative and a positive integer.

Integer rules refer to how we perform operations on integers. This includes addition, subtraction, multiplication, and division. For right now we're going to focus on dividing a negative integer by a positive integer. Division will normally be written one of two ways: $$\begin{align} 15\div3&=5\\ \\ {\text{dividend}\rightarrow\atop \text{divisor}\rightarrow }\frac{15}{3}&=5\leftarrow \text{quotient} \end{align}$$

Division follows the sign rules given by multiplication. $$\begin{align} \frac{+}{+} &= +\\ \\ \frac{-}{-}&=+\\ \\ \frac{+}{-}&=-\\ \\ \frac{-}{+}&=-\end{align}$$ Dividing two numbers with the same sign will give a positive answer, while dividing two numbers with different signs will give a negative answer.

He gives the example $20 \div -4$. We know that the sign of the answer will be negative because we only have one negative sign in the problem. $$20 \div -4 = -5$$

Let's try a practice problem.

The result will always be negative

When you multiply or divide a negative number by a positive number, the answer will always be negative. In fact, any time you have an odd number of negative numbers in a multiplication or division expression, the result will be negative. With that knowledge, all you have to do is divide the numbers as you would if they were both positive, and then add a minus sign.

So with that in mind, here are the steps for dividing a negative number by a positive number:

Step 1: Divide the numbers. Ignore the signs--just pretend you're dividing positive numbers.

Step 2: Deal with the signs. In this case, with one negative number, the result will always be negative.

For example, if we were going to divide $-16$ by $8$, we would first do $16 \div 8 = 2$, then look at the signs (one negative number, so the result would be negative).