Directed Numbers (Negative and positive numbers)

Multiplication of directed numbers

$$\begin{array}{rcr}
1\times 1&=&1\\
-1\times 1&=&-1\\
1\times -1&=&-1\\
-1\times -1&=&1\\
5\times -1&=&-5\\
-6\times 3&=&-18\\
-3\times -5&=&15
\end{array}$$

Addition and Subtraction of directed numbers

$$\begin{array}{rcr}
1 +1&=&2\\
-1+ 1&=&0\\
1+ -1&=&0\\
-1+ -1&=&-2\\
5+ -1&=&4\\
-5+ -1&=&-4\\
-5+1&=&-4\\
5-9&=&-4\\
-5-8&=&-13\\
-15-(-3)&=&-12
\end{array}$$
Notation wise, $a+(-b)$ is written as $a-b$.