Lösung 1.2:2d

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If we divide up the denominators into their smallest possible integer factors,
If we divide up the denominators into their smallest possible integer factors,
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{{Displayed math||<math>\begin{align}
+
{{Abgesetzte Formel||<math>\begin{align}
45&=5\cdot 9=5\cdot 3\cdot 3\,, \\
45&=5\cdot 9=5\cdot 3\cdot 3\,, \\
75&=3\cdot 25=3\cdot 5\cdot 5\,, \\
75&=3\cdot 25=3\cdot 5\cdot 5\,, \\
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the expression can be written as
the expression can be written as
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{{Displayed math||<math>\frac{2}{3\cdot 3\cdot 5}+\frac{1}{3\cdot 5\cdot 5}</math>}}
+
{{Abgesetzte Formel||<math>\frac{2}{3\cdot 3\cdot 5}+\frac{1}{3\cdot 5\cdot 5}</math>}}
and then we see that the denominators have <math>3\cdot 5</math> as a common factor. Therefore, if we multiply the top and bottom of the first fraction by 5
and then we see that the denominators have <math>3\cdot 5</math> as a common factor. Therefore, if we multiply the top and bottom of the first fraction by 5
and the second by 3, the result is the lowest possible denominator
and the second by 3, the result is the lowest possible denominator
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{{Displayed math||<math>\begin{align}
+
{{Abgesetzte Formel||<math>\begin{align}
\frac{2}{3\cdot 3\cdot 5}\cdot \frac{5}{5}+\frac{1}{3\cdot 5\cdot 5}\cdot
\frac{2}{3\cdot 3\cdot 5}\cdot \frac{5}{5}+\frac{1}{3\cdot 5\cdot 5}\cdot
\frac{3}{3} &=\frac{2}{3\cdot 3\cdot 5\cdot 5}
\frac{3}{3} &=\frac{2}{3\cdot 3\cdot 5\cdot 5}

Version vom 08:14, 22. Okt. 2008

If we divide up the denominators into their smallest possible integer factors,

\displaystyle \begin{align} 
45&=5\cdot 9=5\cdot 3\cdot 3\,, \\ 
75&=3\cdot 25=3\cdot 5\cdot 5\,, \\

\end{align}

the expression can be written as

\displaystyle \frac{2}{3\cdot 3\cdot 5}+\frac{1}{3\cdot 5\cdot 5}

and then we see that the denominators have \displaystyle 3\cdot 5 as a common factor. Therefore, if we multiply the top and bottom of the first fraction by 5 and the second by 3, the result is the lowest possible denominator

\displaystyle \begin{align} 
\frac{2}{3\cdot 3\cdot 5}\cdot \frac{5}{5}+\frac{1}{3\cdot 5\cdot 5}\cdot
\frac{3}{3} &=\frac{2}{3\cdot 3\cdot 5\cdot 5}
   +\frac{3}{3\cdot 5\cdot 5\cdot 3}\\[10pt] 
 &= \frac{10}{225}+\frac{3}{225}\,\textrm{.}\\

\end{align}

The lowest common denominator is 225.

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_1.2:2d“