Solution 1.2:4b

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Current revision (10:32, 19 September 2008) (edit) (undo)
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Multiply top and bottom of the double fraction by the reciprocal of the denominator.
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Multiply top and bottom of the double fraction by the reciprocal of the denominator,
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{{Displayed math||<math>\frac{\displaystyle\,\frac{2}{7}\,}{\displaystyle\,\frac{3}{8}\,} = \frac{\displaystyle\,\frac{2}{7}\cdot \frac{8}{3}\,}{\displaystyle\,\frac{\rlap{/}3}{\rlap{/}8}\cdot \frac{\rlap{/}8}{\rlap{/}3}\,}=\frac{2}{7}\cdot \frac{8}{3}\,</math>.}}
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<math>\frac{\frac{2}{7}}{\frac{3}{8}}=\frac{\frac{2}{7}\centerdot \frac{8}{3}}{\frac{3}{8}\centerdot \frac{8}{3}}=\frac{2}{7}\centerdot \frac{8}{3}</math>
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The numerator and denominator on the right-hand side do not have a common factor, so the answer is
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The numerator and denominator on the right-hand side do not have a common factor, so the answer is:
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{{Displayed math||<math>\frac{2}{7}\cdot \frac{8}{3}=\frac{2\cdot 8}{7\cdot 3}=\frac{16}{21}\,</math>.}}
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Note: It is also possible to learn a quick formula for double fractions which says that when the expression is rewritten with just one fraction sign, the denominators in the partial fractions change place,
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<math>\frac{2}{7}\centerdot \frac{8}{3}=\frac{2\centerdot 8}{7\centerdot 3}=\frac{16}{21}</math>
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{{Displayed math||<math>\frac{\displaystyle\,\frac{2}{7}\,}{\displaystyle\,\frac{3}{8}\,}=\frac{2\cdot 8}{3\cdot 7}\,</math>.}}
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NOTE: It is also possible to learn a quick formula for double fractions which says that when the expression is rewritten with just one fraction sign, the denominators in the partial fractions change place:
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<math>\frac{\frac{2}{7}}{\frac{3}{8}}=\frac{2\centerdot 8}{3\centerdot 7}</math>
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Current revision

Multiply top and bottom of the double fraction by the reciprocal of the denominator,

\displaystyle \frac{\displaystyle\,\frac{2}{7}\,}{\displaystyle\,\frac{3}{8}\,} = \frac{\displaystyle\,\frac{2}{7}\cdot \frac{8}{3}\,}{\displaystyle\,\frac{\rlap{/}3}{\rlap{/}8}\cdot \frac{\rlap{/}8}{\rlap{/}3}\,}=\frac{2}{7}\cdot \frac{8}{3}\,.

The numerator and denominator on the right-hand side do not have a common factor, so the answer is

\displaystyle \frac{2}{7}\cdot \frac{8}{3}=\frac{2\cdot 8}{7\cdot 3}=\frac{16}{21}\,.

Note: It is also possible to learn a quick formula for double fractions which says that when the expression is rewritten with just one fraction sign, the denominators in the partial fractions change place,

\displaystyle \frac{\displaystyle\,\frac{2}{7}\,}{\displaystyle\,\frac{3}{8}\,}=\frac{2\cdot 8}{3\cdot 7}\,.
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