\documentclass[a4paper]{article} \usepackage{fullpage} \usepackage{amsmath} \parindent=0in \begin{document} \noindent\textbf{Handout: Addition and Subtraction with Negative Numbers}\\ \noindent\textbf{Secondary 1 Express}\\ \noindent\textbf{Name: }\rule{20em}{0.2pt}\hfill \textbf{Date: }\rule{10em}{0.2pt}\\ \section{Examples of Addition and Subtraction} The following table shows a typical example of what happens when you perform addition and subtraction involving negative numbers. \begin{center} \begin{tabular}{|c|rr|rr|} \hline & \textbf{addition}& & \textbf{subtraction} & \\ \hline \textbf{same sign} & $ 7 + 5 =$ &$ 12 $& $ 7 - 5=$ &$2$ \\ & $ -7 + (-5) =$ &$ -12 $& $ -7 - (-5)=$ &$-2$\\ & & & $ -5 - (-7)=$ &$2$ \\ \hline \textbf{different sign} & $ 7 + (-5)=$ &$ 2 $ & $ 7 - (-5)=$ &$12$ \\ & $ -7 + 5= $ &$ -2$ & $ -7 - 5=$ &$-12$ \\ & & & $ -5 - 7=$ &$-12 $ \\ & & & $ 5 - (-7)=$ &$12 $ \\ \hline \end{tabular} \end{center} Can you understand why in 2 of the boxes above, the answer is consistently either $2$ or $-2$ and in the other 2 boxes, the answer is consistently either $12$ or $-12$? To help you, try counting the number of $(-)$ signs that you see. \section{Commutative Property of Addition} Having the commutative property means that it does not matter which other you perform the operation. For example, \begin{align*} 7 + 5 &= 5 + 7\\ 12 &= 12 \end{align*} Addition is commutative. However, subtraction is not commutative. For example, \begin{align*} 7 -5 &\neq 5 - 7\\ 2 &\neq -2 \end{align*} Can you understand why? \section{Subtracting a negative number} If you subtract a negative number, you will find that this is the same as adding the positive number. For example, \begin{align*} 7 - (-5) &= 7 + 5\\ &= 12 \end{align*} Think of the following analogy: \begin{tabular}{lc} 1. I \underline{want}(+) you to \underline{eat}(+) ice-cream & $ + (+) = +$ \\ 2. I \underline{don't want}(-) you to \underline{eat}(+) ice-cream & $ - (+) = -$ \\ 3. I \underline{want}(+) you to \underline{not eat}(-) ice-cream & $ + (-) = -$ \\ 4. I \underline{don't want}(-) you to \underline{not eat}(-) ice-cream & $ - (-) = +$ \\ \end{tabular} In the second and third statements, I do not wish for you to eat ice-cream. However, in the first and fourth statements, I do wish for you to eat ice-cream. Notice how the double negatives in the fourth statement will cancel each other out? \end{document}