From Förberedande kurs i matematik 1

Revision as of 08:18, 9 September 2008 (edit) Tekbot (Talk | contribs) m (Lösning 1.2:4b moved to Solution 1.2:4b: Robot: moved page) ← Previous diff		Current revision (10:32, 19 September 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	Multiply top and bottom of the double fraction by the reciprocal of the denominator,
-	<center> [[Image:1_2_4b.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	{{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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		+	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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		+	{{Displayed math||<math>\frac{\displaystyle\,\frac{2}{7}\,}{\displaystyle\,\frac{3}{8}\,}=\frac{2\cdot 8}{3\cdot 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}\,.