diff --git a/math-replay/.gitignore b/math-replay/.gitignore new file mode 100644 index 0000000..3eec47d --- /dev/null +++ b/math-replay/.gitignore @@ -0,0 +1,3 @@ +*.aux +*.log +*.pdf diff --git a/math-replay/algebra/order-of-operations.tex b/math-replay/algebra/order-of-operations.tex new file mode 100644 index 0000000..a0ecbc0 --- /dev/null +++ b/math-replay/algebra/order-of-operations.tex @@ -0,0 +1,62 @@ +\documentclass{article} +\begin{document} + +At this point this is mostly LaTeX practice, but why not?!?... + +Related video is at: +http://www.khanacademy.org/math/algebra/solving-linear-equations/v/order-of-operations-example + +1b. +\begin{eqnarray*} +ans & = & 2 + 7 \times 11 - 12 \div 3 \\ +ans & = & 2 + (7 \times 11) - (12 \div 3) \\ +ans & = & 2 + 77 - 4 \\ +ans & = & 79 - 4 \\ +ans & = & 75 +\end{eqnarray*} + +1d. +\begin{eqnarray*} +ans & = & \frac{2 \times (3 + (2 - 1))}{4 - (6 + 2)} - (3 - 5) \\ +ans & = & \frac{2 \times (3 + 1)}{4 - (6 + 2)} - (3 - 5) \\ +ans & = & \frac{2 \times 4}{4 - (6 + 2)} - (3 - 5) \\ +ans & = & \frac{8}{4 - 8} - (3 - 5) \\ +ans & = & \frac{8}{-4} - (3 - 5) \\ +ans & = & -2 - (3 - 5) \\ +ans & = & -2 - -2 \\ +ans & = & -2 + 2 \\ +ans & = & 0 +\end{eqnarray*} + +2b. +\begin{eqnarray*} +ans & = & 2y^2 \mbox{ when } x = 1 \mbox{ and } y = 5 \\ +ans & = & 2 \times (5^2) \\ +ans & = & 2 \times 25 \\ +ans & = & 50 +\end{eqnarray*} + +2d. +\begin{eqnarray*} +ans & = & (y^2 - x)^2 \mbox{ when } x = 2 \mbox{ and } y = 1 \\ +ans & = & (1^2 - 2)^2 \\ +ans & = & (1 - 2)^2 \\ +ans & = & (-1)^2 \\ +ans & = & 1 +\end{eqnarray*} + +3b. +\begin{eqnarray*} +ans & = & \frac{z^2}{x + y} + \frac{x^2}{x - y} \mbox{ when } x = 1, y = -2, \mbox{ and } z = 4 \\ +ans & = & \frac{4^2}{1 + -2} + \frac{1^2}{1 - -2} \\ +ans & = & \frac{16}{-1} + \frac{1}{3} \\ +ans & = & -16 + \frac{1}{3} \\ +ans & = & \frac{-48}{3} + \frac{1}{3} \\ +ans & = & \frac{-47}{3} +\end{eqnarray*} + +3d. +\begin{eqnarray*} +\end{eqnarray*} + +\end{document}