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of negative numbers include measuring temperatures which are below $0$ and bank statements where money which has been withdrawn from an account is shown as negative.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.

Addition and Subtraction

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}

See Also

For more information on all of the topics in this section see our page on numerical reasoning.

Also try these workbooks (these are also very useful for numerical reasoning tests):