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Solution 1.2:2d

From Förberedande kurs i matematik 1

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m (Lösning 1.2:2d moved to Solution 1.2:2d: Robot: moved page)
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If we divide up the denominators into their smallest possible integer factors,
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<center> [[Image:1_2_2d.gif]] </center>
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<math>\begin{align}
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& 45=5\centerdot 9=5\centerdot 3\centerdot 3 \\
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& 75=3\centerdot 25=3\centerdot 5\centerdot 5 \\
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\end{align}</math>
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the expression can be written as
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<math>\frac{1}{5\centerdot 3\centerdot 3}+\frac{1}{3\centerdot 5\centerdot 5}</math>
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and then we see that the denominators have
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<math>3\centerdot 5</math>
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as a common factor. Therefore, if we multiply the top and bottom of the first fraction by
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<math>5</math>
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and the second by
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<math>3</math>
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, the result is the lowest possible denominator.
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<math>\begin{align}
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& \frac{2}{5\centerdot 3\centerdot 3}\centerdot \frac{5}{5}+\frac{1}{3\centerdot 5\centerdot 5}\centerdot \frac{3}{3} \\
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& =\frac{2}{5\centerdot 3\centerdot 3\centerdot 5}+\frac{3}{3\centerdot 5\centerdot 5\centerdot 3} \\
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& =\frac{10}{225}+\frac{3}{225} \\
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\end{align}</math>
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The lowest common denominator is
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<math>225</math>
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.

Revision as of 12:45, 11 September 2008

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


45=59=53375=325=355


the expression can be written as


1533+1355

and then we see that the denominators have 35 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.


253355+135533=25335+33553=10225+3225


The lowest common denominator is 225 .

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