### Numbers: Negative numbers

### Adding and subtracting negative numbers

We have seen that the collection of *integers* consists of positive and negative numbers. Addition and subtraction of positive numbers were considered to be prerequisite knowledge, but adding and subtracting negative numbers will be discussed here.

Adding a negative number means we add something negative. The result will therefore be smaller. We see that adding a negative number is the same as subtracting a positive number.

In symbols: \[\blue{\mathbf{+}} \; \red{\mathbf{-}} \; = \; \red{\mathbf{-}} \]

**Example**

\[\begin{array}{rcl}6\blue{\mathbf{+}}\red{\mathbf{-}}2 &=& 6\red{\mathbf{-}}2 \\ &=&4 \end{array}\]

Subtracting a negative number means that we take something negative away. The result will therefore be bigger. We see that subtracting a negative number is the same as adding a positive number.

In symbols: \[\red{\mathbf{-}} \; \red{\mathbf{-}} \; = \; \blue{\mathbf{+}} \]

**Example**

\[\begin{array}{rcl}6\red{\mathbf{--}}2 &=& 6\blue{\mathbf{+}}2 \\ &=&8 \end{array}\]

# \begin{array}{rcl}

10+{-9}&=&10-9 \\ &&\phantom{xxx}\blue{\text{adding a negative number is the same as subtracting a positive number}} \\

&=& 1 \\ && \phantom{xxx}\blue{\text{subtracted}}

\end {array} #

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