Lösung 1.2:2a

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A common way to calculate the expression in the exercise is to multiply top and bottom of each fraction by the other fraction's denominator, so as to obtain a common denominator,
A common way to calculate the expression in the exercise is to multiply top and bottom of each fraction by the other fraction's denominator, so as to obtain a common denominator,
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{{Displayed math||<math>\frac{1}{6}+\frac{1}{10}=\frac{1}{6}\cdot \frac{10}{10}+\frac{1}{10}\cdot \frac{6}{6}=\frac{10}{60}+\frac{6}{60}\,</math>.}}
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{{Abgesetzte Formel||<math>\frac{1}{6}+\frac{1}{10}=\frac{1}{6}\cdot \frac{10}{10}+\frac{1}{10}\cdot \frac{6}{6}=\frac{10}{60}+\frac{6}{60}\,</math>.}}
However, this gives a common denominator, 60, which is larger than it really needs to be.
However, this gives a common denominator, 60, which is larger than it really needs to be.
If we instead divide up the fractions' denominators into their smallest possible integral factors,
If we instead divide up the fractions' denominators into their smallest possible integral factors,
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{{Displayed math||<math>\frac{1}{2\cdot 3}+\frac{1}{2\cdot 5}\,</math>,}}
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{{Abgesetzte Formel||<math>\frac{1}{2\cdot 3}+\frac{1}{2\cdot 5}\,</math>,}}
we see that both denominators contain the factor 2 and it is then unnecessary to include that factor when we multiply the top and bottom of each fraction.
we see that both denominators contain the factor 2 and it is then unnecessary to include that factor when we multiply the top and bottom of each fraction.
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{{Displayed math||<math>\frac{1}{6}+\frac{1}{10}=\frac{1}{6}\cdot \frac{5}{5}+\frac{1}{10}\cdot \frac{3}{3}=\frac{5}{30}+\frac{3}{30}\,</math>.}}
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{{Abgesetzte Formel||<math>\frac{1}{6}+\frac{1}{10}=\frac{1}{6}\cdot \frac{5}{5}+\frac{1}{10}\cdot \frac{3}{3}=\frac{5}{30}+\frac{3}{30}\,</math>.}}
This gives the lowest common denominator (LCD), 30.
This gives the lowest common denominator (LCD), 30.

Version vom 08:14, 22. Okt. 2008

A common way to calculate the expression in the exercise is to multiply top and bottom of each fraction by the other fraction's denominator, so as to obtain a common denominator,

\displaystyle \frac{1}{6}+\frac{1}{10}=\frac{1}{6}\cdot \frac{10}{10}+\frac{1}{10}\cdot \frac{6}{6}=\frac{10}{60}+\frac{6}{60}\,.

However, this gives a common denominator, 60, which is larger than it really needs to be.

If we instead divide up the fractions' denominators into their smallest possible integral factors,

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

we see that both denominators contain the factor 2 and it is then unnecessary to include that factor when we multiply the top and bottom of each fraction.

\displaystyle \frac{1}{6}+\frac{1}{10}=\frac{1}{6}\cdot \frac{5}{5}+\frac{1}{10}\cdot \frac{3}{3}=\frac{5}{30}+\frac{3}{30}\,.

This gives the lowest common denominator (LCD), 30.

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