Numbers: Negative numbers
Adding and subtracting negative numbers
We have seen that the collection of integers consists of positive and negative numbers. The addition and subtraction of positive numbers were considered prerequisite knowledge, but the addition and subtraction of 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 taking 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}
7+{-5}&=&7-5 \\ &&\phantom{xxx}\blue{\text{adding a negative number is the same as subtracting a positive number}} \\
&=& 2 \\ && \phantom{xxx}\blue{\text{subtracted}}
\end {array} #
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