 # Signs in Math (Positive or Negative)

Here you’ll learn how to work with signs. This is a really important thing to learn.

Signs affect the problems only when you multiply or divide. In regular addition and subtraction problems, the plus and minus will work the same way they did before, like this:

$\begin{array}{llll}\hfill -2+3+4-5& =-2-5+3+4\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =-7+7=0.\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

 $-2+3+4-5=-2-5+3+4=-7+7=0.$

But what happens when you multiply or divide by a negative number?
 $2\cdot \left(-5\right)=\text{?}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\frac{-2}{6}=\text{?}$

In mathematics, we don’t like to write two signs right after each other, like $\cdot -$ or $\cdot +$. To avoid this, we write negative numbers inside parentheses. When we have the parentheses, we don’t need to write the multiplication sign. For example, we may write negative number in this way:

 $2\left(-5\right)=\text{?}\phantom{\rule{2em}{0ex}}\phantom{\rule{2em}{0ex}}\left(-1\right)\left(-5\right)=\text{?}$

Between a number and a parentheses, there’s an invisible multiplication sign. There’s one between two parentheses next to each other as well.

Rule

### Signs

When you have the same sign twice ($++$ or $--$), they’ll turn into a single plus sign ($+$).

When you have different signs ($+-$ or $-+$), they’ll turn into a single minus sign ($-$).

Multiplication and division follow the relationships between numbers we know from the multiplication table. But how do you take the sign into consideration? The answer to that comes here.

When I multiply or divide by negative or positive numbers, a smart trick I use is to think “SIGN NUMBER”, in that order. This means that I always find the sign first, then the number afterwards.

In the examples below, you’ll see that I write a $+$ in front of the positive numbers to demonstrate how I think. When I work with these problems, I have to remember that there’s an invisible $+$ in front of all positive numbers.

In the first example below, I’ll show you a nice way to think about the problems. In the second example below, you can see how you should be writing them down. There are some hidden operations, but the most important thing is that you understand the way of thinking.

Example 1

### HowtoThinkWhenSolvingProblems

Calculate: $\begin{array}{llll}\hfill 2\cdot \left(-5\right)& =+2\cdot \left(-5\right)\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =+-2\cdot 5\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =-10\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Calculate: $\begin{array}{llll}\hfill -2\cdot \left(-5\right)& =--2\cdot 5\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =+10\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =10\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Calculate: $\begin{array}{llll}\hfill 2\cdot 5& =+2\cdot \left(+5\right)\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =++2\cdot 5\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =+10\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =10\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Calculate: $\begin{array}{llll}\hfill -2\cdot 5& =-2\cdot \left(+5\right)\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =-+2\cdot 5\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =-10\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Example 2

### HowtoWriteYourSolutions

Calculate:

 $2\left(-5\right)=-10$

Calculate:

 $-2\left(-5\right)=10$

Calculate:

 $2\cdot 5=10$

Calculate:

 $-2\cdot 5=-10$

If you want to practice more, I recommend that you watch instructional videos about multiplying negative numbers.