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*}