Solution 1.2:2d
From Förberedande kurs i matematik 1
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the expression can be written as | the expression can be written as | ||
- | {{Displayed math||<math>\frac{ | + | {{Displayed math||<math>\frac{2}{3\cdot 3\cdot 5}+\frac{1}{3\cdot 5\cdot 5}</math>}} |
and then we see that the denominators have <math>3\cdot 5</math> as a common factor. Therefore, if we multiply the top and bottom of the first fraction by 5 | and then we see that the denominators have <math>3\cdot 5</math> as a common factor. Therefore, if we multiply the top and bottom of the first fraction by 5 | ||
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{{Displayed math||<math>\begin{align} | {{Displayed math||<math>\begin{align} | ||
- | \frac{2}{ | + | \frac{2}{3\cdot 3\cdot 5}\cdot \frac{5}{5}+\frac{1}{3\cdot 5\cdot 5}\cdot |
- | \frac{3}{3} &=\frac{2}{ | + | \frac{3}{3} &=\frac{2}{3\cdot 3\cdot 5\cdot 5} |
+\frac{3}{3\cdot 5\cdot 5\cdot 3}\\[10pt] | +\frac{3}{3\cdot 5\cdot 5\cdot 3}\\[10pt] | ||
&= \frac{10}{225}+\frac{3}{225}\,\textrm{.}\\ | &= \frac{10}{225}+\frac{3}{225}\,\textrm{.}\\ |
Current revision
If we divide up the denominators into their smallest possible integer factors,
\displaystyle \begin{align}
45&=5\cdot 9=5\cdot 3\cdot 3\,, \\ 75&=3\cdot 25=3\cdot 5\cdot 5\,, \\ \end{align} |
the expression can be written as
\displaystyle \frac{2}{3\cdot 3\cdot 5}+\frac{1}{3\cdot 5\cdot 5} |
and then we see that the denominators have \displaystyle 3\cdot 5 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
\displaystyle \begin{align}
\frac{2}{3\cdot 3\cdot 5}\cdot \frac{5}{5}+\frac{1}{3\cdot 5\cdot 5}\cdot \frac{3}{3} &=\frac{2}{3\cdot 3\cdot 5\cdot 5} +\frac{3}{3\cdot 5\cdot 5\cdot 3}\\[10pt] &= \frac{10}{225}+\frac{3}{225}\,\textrm{.}\\ \end{align} |
The lowest common denominator is 225.