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94 lines
2.2 KiB
94 lines
2.2 KiB
\documentclass{article}
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\begin{document}
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At this point this is mostly LaTeX practice, but why not?!?...
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Related video is at:
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http://www.khanacademy.org/math/algebra/solving-linear-equations/v/order-of-operations-example
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1b.
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\begin{eqnarray*}
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ans & = & 2 + 7 \times 11 - 12 \div 3 \\
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ans & = & 2 + (7 \times 11) - (12 \div 3) \\
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ans & = & 2 + 77 - 4 \\
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ans & = & 79 - 4 \\
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ans & = & 75
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\end{eqnarray*}
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1d.
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\begin{eqnarray*}
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ans & = & \frac{2 \times (3 + (2 - 1))}{4 - (6 + 2)} - (3 - 5) \\
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ans & = & \frac{2 \times (3 + 1)}{4 - (6 + 2)} - (3 - 5) \\
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ans & = & \frac{2 \times 4}{4 - (6 + 2)} - (3 - 5) \\
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ans & = & \frac{8}{4 - 8} - (3 - 5) \\
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ans & = & \frac{8}{-4} - (3 - 5) \\
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ans & = & -2 - (3 - 5) \\
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ans & = & -2 - -2 \\
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ans & = & -2 + 2 \\
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ans & = & 0
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\end{eqnarray*}
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2b.
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\begin{eqnarray*}
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ans & = & 2y^2 \mbox{ when } x = 1 \mbox{ and } y = 5 \\
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ans & = & 2 \times (5^2) \\
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ans & = & 2 \times 25 \\
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ans & = & 50
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\end{eqnarray*}
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2d.
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\begin{eqnarray*}
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ans & = & (y^2 - x)^2 \mbox{ when } x = 2 \mbox{ and } y = 1 \\
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ans & = & (1^2 - 2)^2 \\
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ans & = & (1 - 2)^2 \\
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ans & = & (-1)^2 \\
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ans & = & 1
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\end{eqnarray*}
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3b.
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\begin{eqnarray*}
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ans & = & \frac{z^2}{x + y} + \frac{x^2}{x - y} \mbox{ when } x = 1, y = -2, \mbox{ and } z = 4 \\
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ans & = & \frac{4^2}{1 + -2} + \frac{1^2}{1 - -2} \\
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ans & = & \frac{16}{-1} + \frac{1}{3} \\
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ans & = & -16 + \frac{1}{3} \\
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ans & = & \frac{-48}{3} + \frac{1}{3} \\
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ans & = & \frac{-47}{3}
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\end{eqnarray*}
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3d.
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\begin{eqnarray*}
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ans & = & \frac{x^2 - z^2}{xz - 2x(z - x)} \mbox{ when } x = -1 \mbox{ and } z = 3 \\
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ans & = & \frac{-1^2 - 3^2}{-1 \times 3 - 2 \times -1 \times (3 - -1)} \\
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ans & = & \frac{1 - 9}{-3 - 2(-1) \times 4} \\
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ans & = & \frac{-8}{-3 - -2 \times 4} \\
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ans & = & \frac{-8}{-3 - -8} \\
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ans & = & \frac{-8}{5}
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\end{eqnarray*}
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4b.
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\begin{eqnarray*}
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12 \div 4 + 10 - 3 \times 3 + 7 & = & 11 \\
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3 + 10 - 9 + 7 & = & 11 \\
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13 - 9 + 7 & = & 11 \\
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4 + 7 & = & 11 \\
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11 & = & 11
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\end{eqnarray*}
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4d.
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\begin{eqnarray*}
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12 - 8 - 4 \times 5 & = & -8 \\
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12 - 8 - 20 & = & -8 \\
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4 - 20 & = & -8 \\
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-16 & = & -8
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\end{eqnarray*}
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\begin{eqnarray*}
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12 - 8 - 4 \times 5 & = & -8 \\
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12 - (8 - 4) \times 5 & = & -8 \\
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12 - 4 \times 5 & = & -8 \\
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12 - 20 & = & -8 \\
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-8 & = & -8
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\end{eqnarray*}
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\end{document}
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