Solution 1.2:2a
From Förberedande kurs i matematik 1
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A common way to calculate the expression in the exercise is to multiply top and bottom of each fraction by the other fraction's denominator, so as to obtain a common denominator, | A common way to calculate the expression in the exercise is to multiply top and bottom of each fraction by the other fraction's denominator, so as to obtain a common denominator, | ||
| - | + | {{Displayed math||<math>\frac{1}{6}+\frac{1}{10}=\frac{1}{6}\cdot \frac{10}{10}+\frac{1}{10}\cdot \frac{6}{6}=\frac{10}{60}+\frac{6}{60}\,</math>.}} | |
| - | <math>\frac{1}{6}+\frac{1}{10}=\frac{1}{6}\ | + | |
However, this gives a common denominator, 60, which is larger than it really needs to be. | However, this gives a common denominator, 60, which is larger than it really needs to be. | ||
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If we instead divide up the fractions' denominators into their smallest possible integral factors, | If we instead divide up the fractions' denominators into their smallest possible integral factors, | ||
| - | + | {{Displayed math||<math>\frac{1}{2\cdot 3}+\frac{1}{2\cdot 5}\,</math>,}} | |
| - | <math>\frac{1}{2\ | + | |
we see that both denominators contain the factor 2 and it is then unnecessary to include that factor when we multiply the top and bottom of each fraction. | we see that both denominators contain the factor 2 and it is then unnecessary to include that factor when we multiply the top and bottom of each fraction. | ||
| - | + | {{Displayed math||<math>\frac{1}{6}+\frac{1}{10}=\frac{1}{6}\cdot \frac{5}{5}+\frac{1}{10}\cdot \frac{3}{3}=\frac{5}{30}+\frac{3}{30}\,</math>.}} | |
| - | <math>\frac{1}{6}+\frac{1}{10}=\frac{1}{6}\ | + | |
| - | + | ||
This gives the lowest common denominator (LCD), 30. | This gives the lowest common denominator (LCD), 30. | ||
Current revision
A common way to calculate the expression in the exercise is to multiply top and bottom of each fraction by the other fraction's denominator, so as to obtain a common denominator,
| \displaystyle \frac{1}{6}+\frac{1}{10}=\frac{1}{6}\cdot \frac{10}{10}+\frac{1}{10}\cdot \frac{6}{6}=\frac{10}{60}+\frac{6}{60}\,. |
However, this gives a common denominator, 60, which is larger than it really needs to be.
If we instead divide up the fractions' denominators into their smallest possible integral factors,
| \displaystyle \frac{1}{2\cdot 3}+\frac{1}{2\cdot 5}\,, |
we see that both denominators contain the factor 2 and it is then unnecessary to include that factor when we multiply the top and bottom of each fraction.
| \displaystyle \frac{1}{6}+\frac{1}{10}=\frac{1}{6}\cdot \frac{5}{5}+\frac{1}{10}\cdot \frac{3}{3}=\frac{5}{30}+\frac{3}{30}\,. |
This gives the lowest common denominator (LCD), 30.
