### Positive and Negative Numbers

Positive numbers are those which are greater than zero $(\gt 0)$. Negative numbers are those which are less than zero $(\lt 0)$. Examples of real-world uses of negative numbers include measuring temperatures which are below $0$ and bank statements where money which has been withdrawn from an account is shown as negative.

When using positive and negative numbers we put a $+$ sign in front of positive numbers and a $-$ sign in front of negative numbers. If there is no sign in front of a number it typically means that the number is positive.

For example, $+2$ is positive, $-2$ is negative, and $2$ is positive.

A $+$ sign between two numbers means that we are adding the numbers. A $-$ sign between two numbers means that we are subtracting the second number from the first.

For addition and subtraction of positive and negative numbers we can use the following rules:

• Two of the same signs $(+ \text{ and } + \text{ or } - \text{ and } -)$ become a positive sign $(+)$,
• Two different signs $(+ \text{ and } - \text{ in either order})$ become a negative sign $(-)$,
• One sign on its own $(+ \text{ or } -)$ does not change.

For example, \begin{align} 5+(−4)=5-4&=1\\ 11−(−3)=11+3&=14\\ 10+5&=15 \end{align}

#### Multiplication and Division

For multiplication and division of positive and negative numbers we can use the following rules to determine the sign of the answer:

\begin{array}{ccccc} \text{Positive} & \times / \div & \text{Positive} & = & \text{Positive} \\ \text{Negative} & \times / \div & \text{Negative} & = & \text{Positive} \\ \text{Positive} & \times / \div & \text{Negative} & = & \text{Negative} \\ \text{Negative} & \times / \div & \text{Positive} & = & \text{Negative} \\ \end{array}

For example, \begin{align} (+10) \times (+1)&=(+10)\\ \frac{(+10)}{(-2)}&=(-5)\\ \frac{(-2)}{1}&=-2\\ (-5) \times(-20)&=100 \end{align}