Question

$$\frac{ 3 }{ 5 } \frac{ \times }{ \frac{ 6 }{ 9 } }$$

Answer

$$(9*^2)/10$$

Solution


Simplify  \(\frac{6}{9}\)  to  \(\frac{2}{3}\).
\[\frac{3}{5}\times \frac{}{\frac{2}{3}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{3}{5\times \frac{2}{3}}\]
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{3}{\frac{5\times 2}{3}}\]
Simplify  \(5\times 2\)  to  \(10\).
\[\frac{3}{\frac{10}{3}}\]
Invert and multiply.
\[3\times \frac{3}{10}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{3\times 3}{10}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{{3}^{2}{}^{2}}{10}\]
Simplify  \({3}^{2}\)  to  \(9\).
\[\frac{9{}^{2}}{10}\]