Aus Online Mathematik Brückenkurs 1

We begin by calculating the numerator in the main fraction:

\displaystyle \frac{2}{\frac{1}{7}-\frac{1}{15}}=\frac{2}{\frac{1\centerdot 15}{7\centerdot 15}-\frac{1\centerdot 7}{15\centerdot 7}}=\frac{2}{\frac{15-7}{7\centerdot 15}}=\frac{2}{\frac{8}{7\centerdot 15}}

Note that we keep \displaystyle 7\centerdot 15 as it is, and do not multiply it to give \displaystyle 105 , because this will make the task of cancellation later simpler. We calculate the fraction on the right-hand side by multiplying top and bottom by \displaystyle 7\centerdot {15}/{8}\;

\displaystyle \frac{2}{\frac{8}{7\centerdot 15}}=\frac{2\centerdot \frac{7\centerdot 5}{8}}{\frac{8}{7\centerdot 15}\centerdot \frac{7\centerdot 5}{8}}=\frac{2\centerdot 7\centerdot 15}{8}

If we now divide up \displaystyle 8 and \displaystyle 15 into their smallest possible integer factors, \displaystyle 8=2\centerdot 2\centerdot 2 and \displaystyle 15=3\centerdot 5 , we see that the answer in simplified form will be

\displaystyle \frac{2\centerdot 7\centerdot 15}{8}=\frac{2\centerdot 7\centerdot 3\centerdot 5}{2\centerdot 2\centerdot 2}=\frac{7\centerdot 3\centerdot 5}{2\centerdot 2}=\frac{105}{4}