Aus Online Mathematik Brückenkurs 1

The denominator in the expression has \displaystyle 10 as a common factor,

\displaystyle \frac{3}{2\centerdot 10}+\frac{7}{5\centerdot 10}-\frac{1}{10}

and it is therefore sufficient to multiply the top and bottom of each fraction by the other factors in the denominators in order to obtain a common denominator,

\displaystyle \frac{3\centerdot 5}{20\centerdot 5}+\frac{7\centerdot 2}{50\centerdot 2}-\frac{1\centerdot 5\centerdot 2}{10\centerdot 5\centerdot 2}=\frac{15}{100}+\frac{14}{100}-\frac{10}{100}

The lowest common denominator (LCD) is therefore \displaystyle 100 , and the expression is equal to

\displaystyle \frac{15}{100}+\frac{14}{100}-\frac{10}{100}=\frac{15+14-10}{100}=\frac{19}{100}