Solution 1.2:4a

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Current revision (08:51, 19 September 2008) (edit) (undo)
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*****REVISE***
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We calculate the double fraction by multiplying top and bottom by the reciprocal of the denominator,
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We calculate the double fraction by multiplying top and bottom by the reciprocal of the denominator:
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{{Displayed math||<math>\frac{\displaystyle\ \frac{3}{5}\vphantom{\Biggl(}\ }{\displaystyle\ \frac{7}{10}\vphantom{\Biggl(}\ } = \frac{\displaystyle\frac{3}{5}\cdot\frac{10}{7}\vphantom{\Biggl(}}{\displaystyle \frac{\rlap{/}7}{\rlap{\,/}10}\cdot \frac{\rlap{\,/}10}{\rlap{/}7}\vphantom{\Biggl(}} = \frac{3}{5}\cdot \frac{10}{7}\,</math>.}}
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<math>\frac{\frac{3}{5}}{\frac{7}{10}}=\frac{\frac{3}{5}\centerdot \frac{10}{7}}{\frac{7}{10}\centerdot \frac{10}{7}}=\frac{3}{5}\centerdot \frac{10}{7}</math>
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The expression can now be simplified further by removing the common factor
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<math>5</math>
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The expression can now be simplified further by removing the common factor 5,
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<math>\frac{3}{5}\centerdot \frac{10}{7}=\frac{3}{5}\centerdot \frac{2\centerdot 5}{7}=\frac{3\centerdot 2}{7}=\frac{6}{7}</math>
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{{Displayed math||<math>\frac{3}{5}\cdot \frac{10}{7} = \frac{3}{\rlap{/}5}\cdot \frac{2\cdot {}\rlap{/}5}{7} = \frac{3\cdot 2}{7} = \frac{6}{7}\,</math>.}}

Current revision

We calculate the double fraction by multiplying top and bottom by the reciprocal of the denominator,

\displaystyle \frac{\displaystyle\ \frac{3}{5}\vphantom{\Biggl(}\ }{\displaystyle\ \frac{7}{10}\vphantom{\Biggl(}\ } = \frac{\displaystyle\frac{3}{5}\cdot\frac{10}{7}\vphantom{\Biggl(}}{\displaystyle \frac{\rlap{/}7}{\rlap{\,/}10}\cdot \frac{\rlap{\,/}10}{\rlap{/}7}\vphantom{\Biggl(}} = \frac{3}{5}\cdot \frac{10}{7}\,.

The expression can now be simplified further by removing the common factor 5,

\displaystyle \frac{3}{5}\cdot \frac{10}{7} = \frac{3}{\rlap{/}5}\cdot \frac{2\cdot {}\rlap{/}5}{7} = \frac{3\cdot 2}{7} = \frac{6}{7}\,.
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