Example1.1.7Adding One Number of Each Sign

Here are four examples of addition where one number is positive and the other is negative.

1. $$-15+12$$

We have one number of each sign, with sizes $$15$$ and $$12\text{.}$$ Their difference is $$3\text{.}$$ But of the two numbers, the negative number dominated. So the result from adding these is $$-3\text{:}$$

\begin{equation*} -15+12=-3 \end{equation*}
2. $$200+(-100)$$

We have one number of each sign, with sizes $$200$$ and $$100\text{.}$$ Their difference is $$100\text{.}$$ But of the two numbers, the positive number dominated. So the result from adding these is $$100\text{:}$$

\begin{equation*} 200+(-100)=100 \end{equation*}
3. $$12.8+(-20)$$

We have one number of each sign, with sizes $$12.8$$ and $$20\text{.}$$ Their difference is $$7.2\text{.}$$ But of the two numbers, the negative number dominated. So the result from adding these is $$-7.2\text{:}$$

\begin{equation*} 12.8+(-20)=-7.2 \end{equation*}
4. $$-87.3+87.3$$

We have one number of each sign, both with size $$87.3\text{.}$$ The opposing forces cancel each other, leaving a result of $$0\text{:}$$

\begin{equation*} -87.3+87.3=0 \end{equation*}
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