Question

$$\frac{1}{2}Of\frac{2}{5}\div\frac{3}{15}\times\frac{7}{15}\times\frac{6}{7}(1\frac{1}{2}\times\frac{1}{2})$$

Answer

(11*Of)/10

Solution


Simplify  \(\frac{3}{15}\)  to  \(\frac{1}{5}\).
\[\frac{1}{2}Of\times \frac{\frac{2}{5}}{\frac{1}{5}}\times \frac{7}{15}\times \frac{6}{7}(\frac{11}{2}\times \frac{1}{2})\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{1}{2}Of\times \frac{\frac{2}{5}}{\frac{1}{5}}\times \frac{7}{15}\times \frac{6}{7}\times \frac{11\times 1}{2\times 2}\]
Simplify  \(11\times 1\)  to  \(11\).
\[\frac{1}{2}Of\times \frac{\frac{2}{5}}{\frac{1}{5}}\times \frac{7}{15}\times \frac{6}{7}\times \frac{11}{2\times 2}\]
Simplify  \(2\times 2\)  to  \(4\).
\[\frac{1}{2}Of\times \frac{\frac{2}{5}}{\frac{1}{5}}\times \frac{7}{15}\times \frac{6}{7}\times \frac{11}{4}\]
Cancel \(7\).
\[\frac{1}{2}Of\times \frac{2}{5\times \frac{1}{5}}\times \frac{1}{15}\times 6\times \frac{11}{4}\]
Cancel \(5\).
\[\frac{1}{2}Of\times \frac{2}{1}\times \frac{1}{15}\times 6\times \frac{11}{4}\]
Cancel \(2\).
\[Of\times \frac{1}{15}\times 6\times \frac{11}{4}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{Of\times 1\times 6\times 11}{15\times 4}\]
Simplify  \(Of\times 1\)  to  \(Of\).
\[\frac{Of\times 6\times 11}{15\times 4}\]
Simplify  \(Of\times 6\)  to  \(6Of\).
\[\frac{6Of\times 11}{15\times 4}\]
Simplify  \(6Of\times 11\)  to  \(66Of\).
\[\frac{66Of}{15\times 4}\]
Simplify  \(15\times 4\)  to  \(60\).
\[\frac{66Of}{60}\]
Simplify.
\[\frac{11Of}{10}\]