Expansion/Simplifying, Addition/Subtraction, and Multiplication/Division of fractions.
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Concept |
Content |
Numbers |
Introducing numbers: from natural numbers to real numbers. |
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The following identities hold:
Expansion/Simplifying: \(\displaystyle{\frac{a}{b} = \frac{a \cdot c}{b
\cdot c} }\)
Example 1. \[\frac{1}{2}
= \frac{2}{4}\]
Addition/Subtraction: \(\displaystyle{\frac{a}{b} \pm \frac{c}{d} =
\frac{ad\pm bc}{bd}}\)
Example 2. \[\frac{2}{5}
+ \frac{3}{4} = \frac{2\cdot 4}{5\cdot 4} + \frac{3\cdot 5}{4\cdot 5} =
\frac{8+15}{20} = \frac{23}{20}\]
Multiplication/Division: \(\displaystyle{\frac{a}{b} \cdot \frac{c}{d} =
\frac{ac}{bd}}\quad\) and \(\quad
\displaystyle{\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b} \cdot
\frac{d}{c} = \frac{ad}{bc}}\)
Example 3. \[\frac{3}{4}\cdot \frac{2}{3} = \frac{3 \cdot
2}{4\cdot 3} = \frac{2}{4} = \frac{1}{2}\]
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