Processing Math: Done
Solution 1.2:2c
From Förberedande kurs i matematik 1
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| - | {{ | + | We divide up the two numerators into the smallest possible integer factors, |
| - | < | + | |
| - | {{ | + | {{Displayed math||<math>\begin{align} |
| + | 12 &= 2\cdot 6 = 2\cdot 2\cdot 3\,,\\ | ||
| + | 14 &= 2\cdot 7\,\textrm{.} \\ | ||
| + | \end{align}</math>}} | ||
| + | |||
| + | The expression can thus be written as | ||
| + | |||
| + | {{Displayed math|| | ||
| + | <math>\frac{1}{2\cdot 2\cdot 3}-\frac{1}{2\cdot 7}\,</math>.}} | ||
| + | |||
| + | 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> | ||
| + | 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>, | ||
| + | |||
| + | {{Displayed math||<math>\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}</math>}} | ||
| + | |||
| + | The lowest common denominator is 84. | ||
Current revision
We divide up the two numerators into the smallest possible integer factors,
 6=223 =27. |
The expression can thus be written as
|
|
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 3237
| 23−127=122377−1272323=72237−232237=784−684. |
The lowest common denominator is 84.
