### Numbers: Negative numbers

### Absolute value

We have now seen that there are positive and negative numbers and we also know how to perform calculations with them. In some cases we only want to consider positive numbers. To do so, we use the absolute value.

The **absolute value** of #\green5# equals #\green5# and the absolute value of #\blue{-5}# also equals #\green{5}#.

We write this as #\abs{\green5}=\abs{\blue{-5}}=\green5#. The vertical bars represent the **absolute value**.

In general, the absolute value of a number is equal to:

\[\begin{cases} \phantom{x} \text{its opposite} & \mbox{ if } \text{the number is negative } \\ \phantom{x} \text{the number itself} & \mbox{ if } \text{the number is non-negative} \end{cases}\]

**Examples**

\[\begin{array}{rcl}\abs{-65}&=& 65 \\ \\ \abs{89}&=&89 \\ \\ \abs{12-19}&=&\abs{-7}\\&=&7 \end{array}\]

The absolute value of a number is equal to:

\[\begin{cases} \phantom{x} \text{its opposite} & \mbox{ if } \text{the number is negative } \\ \phantom{x} \text{the number itself} & \mbox{ if } \text{the number is non-negative} \end{cases}\]

In this case the number is non-negative. Therefore, #\abs{5}=5#.

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