Solution 1.2:2c

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We divide up the two numerators into the smallest possible integer factors,
We divide up the two numerators into the smallest possible integer factors,
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{{Displayed math||<math>\begin{align}
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<math>\begin{align}
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12 &= 2\cdot 6 = 2\cdot 2\cdot 3\,,\\
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& 12=2\centerdot 6=2\centerdot 2\centerdot 3 \\
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14 &= 2\cdot 7\,\textrm{.} \\
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& 14=2\centerdot 7 \\
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\end{align}</math>}}
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\end{align}</math>
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The expression can thus be written as
The expression can thus be written as
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{{Displayed math||
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<math>\frac{1}{2\cdot 2\cdot 3}-\frac{1}{2\cdot 7}\,</math>.}}
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<math>\frac{1}{2\centerdot 2\centerdot 3}-\frac{1}{2\centerdot 7}</math>
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Here, we see that the denominators have a factor 2 in common. We multiply the top and bottom of the first fraction by 7 and the second by <math>2\cdot 3</math>
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i.e. we leave out the common factor 2, so that the fractions have the lowest common denominator <math>2\cdot 2\cdot 3\cdot 7</math>,
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Here, we see that the denominators have a factor
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<math>2</math>
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in common. We multiply the top and bottom of the first fraction by
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<math>7</math>
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and the second by
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<math>2\centerdot 3</math>
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i.e. we leave out the common factor
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<math>2</math>, so that the fractions have the lowest common denominator
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<math>2\centerdot 2\centerdot 3\centerdot 7</math>,
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<math>\frac{1}{12}-\frac{1}{14}=\frac{1}{2\centerdot 2\centerdot 3}-\frac{1}{2\centerdot 7}=\frac{1}{2\centerdot 2\centerdot 3}\centerdot \frac{7}{7}-\frac{1}{2\centerdot 7}\centerdot \frac{2\centerdot 3}{2\centerdot 3}</math>
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{{Displayed math||<math>\begin{align}
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\frac{1}{12}-\frac{1}{14} &= \frac{1}{2\cdot 2\cdot 3}-\frac{1}{2\cdot 7}\\[5pt]
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&= \frac{1}{2\cdot 2\cdot 3}\cdot \frac{7}{7}-\frac{1}{2\cdot 7}\cdot \frac{2\cdot 3}{2\cdot 3}\\[5pt]
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&= \frac{7}{2\cdot 2\cdot 3\cdot 7} - \frac{2\cdot 3}{2\cdot 2\cdot 3\cdot 7}\\[5pt]
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&= \frac{7}{84} - \frac{6}{84}\,\textrm{.}
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\end{align}</math>}}
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The lowest common denominator is
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The lowest common denominator is 84.
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<math>84</math>.
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Current revision

We divide up the two numerators into the smallest possible integer factors,

\displaystyle \begin{align}

12 &= 2\cdot 6 = 2\cdot 2\cdot 3\,,\\ 14 &= 2\cdot 7\,\textrm{.} \\ \end{align}

The expression can thus be written as

\displaystyle \frac{1}{2\cdot 2\cdot 3}-\frac{1}{2\cdot 7}\,.

Here, we see that the denominators have a factor 2 in common. We multiply the top and bottom of the first fraction by 7 and the second by \displaystyle 2\cdot 3 i.e. we leave out the common factor 2, so that the fractions have the lowest common denominator \displaystyle 2\cdot 2\cdot 3\cdot 7,

\displaystyle \begin{align}

\frac{1}{12}-\frac{1}{14} &= \frac{1}{2\cdot 2\cdot 3}-\frac{1}{2\cdot 7}\\[5pt] &= \frac{1}{2\cdot 2\cdot 3}\cdot \frac{7}{7}-\frac{1}{2\cdot 7}\cdot \frac{2\cdot 3}{2\cdot 3}\\[5pt] &= \frac{7}{2\cdot 2\cdot 3\cdot 7} - \frac{2\cdot 3}{2\cdot 2\cdot 3\cdot 7}\\[5pt] &= \frac{7}{84} - \frac{6}{84}\,\textrm{.} \end{align}

The lowest common denominator is 84.

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