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Solution 1.2:2d

From Förberedande kurs i matematik 1

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Current revision (12:21, 22 September 2008) (edit) (undo)
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Line 8: Line 8:
the expression can be written as
the expression can be written as
-
{{Displayed math||<math>\frac{1}{5\cdot 3\cdot 3}+\frac{1}{3\cdot 5\cdot 5}</math>}}
+
{{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
Line 14: Line 14:
{{Displayed math||<math>\begin{align}
{{Displayed math||<math>\begin{align}
-
\frac{2}{5\cdot 3\cdot 3}\cdot \frac{5}{5}+\frac{1}{3\cdot 5\cdot 5}\cdot
+
\frac{2}{3\cdot 3\cdot 5}\cdot \frac{5}{5}+\frac{1}{3\cdot 5\cdot 5}\cdot
-
\frac{3}{3} &=\frac{2}{5\cdot 3\cdot 3\cdot 5}
+
\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,

4575=59=533=325=355

the expression can be written as

2335+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

233555+135533=23355+33553=10225+3225.

The lowest common denominator is 225.

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