Lösung 1.2:3b

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If we divide the denominators in succession by
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If we divide the denominators in succession by 2, we see that
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<math>2</math>
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, we see that
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{{Displayed math||<math>\begin{align}
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24&=2\cdot 2\cdot 2\cdot 3\,,\\
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40&=2\cdot 2\cdot 2\cdot 5\,,\\
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16&=2\cdot 2\cdot 2\cdot 2\,,\\
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\end{align}</math>}}
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<math>\begin{align}
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i.e. they all have a factor <math>2\cdot 2\cdot 2=8</math> in common,
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& 24=2\centerdot 2\centerdot 2\centerdot 3 \\
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& 40=2\centerdot 2\centerdot \centerdot 5 \\
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& 16=2\centerdot 2\centerdot 2\centerdot 2 \\
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\end{align}</math>
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{{Displayed math||<math>\frac{1}{3\cdot 8}+\frac{1}{5\cdot 8}-\frac{1}{2\cdot 8}\,</math>.}}
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i.e. they all have a factor
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Hence we do not need to take 8 as a factor when we multiply the top and bottom of each fraction by the product of the other fractions' denominators, but instead we
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<math>2\centerdot 2\centerdot 2=8</math>
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obtain the lowest common denominator by multiplying top and bottom by the other factors, 2, 3 and 5,
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in common,
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{{Displayed math||<math>\frac{1\cdot 2\cdot 5}{3\cdot 8\cdot 2\cdot 5}+\frac{1\cdot 2\cdot 3}{5\cdot 8\cdot 2\cdot 3}-\frac{1\cdot 3\cdot 5}{2\cdot 8\cdot 3\cdot 5}=\frac{10}{240}+\frac{6}{240}-\frac{15}{240}\,</math>.}}
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The LCD is 240 and the answer is
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<math>\frac{1}{3\centerdot 8}+\frac{1}{5\centerdot 8}-\frac{1}{2\centerdot 8}</math>
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{{Displayed math||<math>\frac{10}{240}+\frac{6}{240}-\frac{15}{240}=\frac{10+6-15}{240}=\frac{1}{240}\,</math>.}}
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,
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and hence we do not need to take
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<math>8</math>
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as a factor when we multiply the top and bottom of each fraction by the product of the other fractions' denominators, but instead we
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obtain the lowest common denominator by multiplying top and bottom by the other factors,
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<math>2,\ 3</math>
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and
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<math>5</math>
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:
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<math>\frac{1\centerdot 2\centerdot 5}{3\centerdot 8\centerdot 2\centerdot 5}+\frac{1\centerdot 2\centerdot 3}{5\centerdot 8\centerdot 2\centerdot 3}-\frac{1\centerdot 3\centerdot 5}{2\centerdot 8\centerdot 3\centerdot 5}=\frac{10}{240}+\frac{6}{240}-\frac{15}{240}</math>
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The LCD is
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<math>240</math>
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and the answer is
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<math>\frac{10}{240}+\frac{6}{240}-\frac{15}{240}=\frac{10+6-15}{240}=\frac{1}{240}</math>
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Version vom 08:42, 19. Sep. 2008

If we divide the denominators in succession by 2, we see that

Vorlage:Displayed math

i.e. they all have a factor \displaystyle 2\cdot 2\cdot 2=8 in common,

Vorlage:Displayed math

Hence we do not need to take 8 as a factor when we multiply the top and bottom of each fraction by the product of the other fractions' denominators, but instead we obtain the lowest common denominator by multiplying top and bottom by the other factors, 2, 3 and 5,

Vorlage:Displayed math

The LCD is 240 and the answer is

Vorlage:Displayed math

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_1.2:3b“