Solution 1.2:2d

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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,


\displaystyle \begin{align} & 45=5\centerdot 9=5\centerdot 3\centerdot 3 \\ & 75=3\centerdot 25=3\centerdot 5\centerdot 5 \\ \end{align}


the expression can be written as


\displaystyle \frac{1}{5\centerdot 3\centerdot 3}+\frac{1}{3\centerdot 5\centerdot 5}

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


\displaystyle \begin{align} & \frac{2}{5\centerdot 3\centerdot 3}\centerdot \frac{5}{5}+\frac{1}{3\centerdot 5\centerdot 5}\centerdot \frac{3}{3} \\ & =\frac{2}{5\centerdot 3\centerdot 3\centerdot 5}+\frac{3}{3\centerdot 5\centerdot 5\centerdot 3} \\ & =\frac{10}{225}+\frac{3}{225} \\ \end{align}


The lowest common denominator is \displaystyle 225 .

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