Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{\frac{1\times \sqrt{2}\times 1}{2\times 2}}{\frac{4}{5}\times \frac{\sqrt{2}}{2}\times \frac{5}{4}}\]
Simplify \(1\times \sqrt{2}\times 1\) to \(\sqrt{2}\).
\[\frac{\frac{\sqrt{2}}{2\times 2}}{\frac{4}{5}\times \frac{\sqrt{2}}{2}\times \frac{5}{4}}\]
Simplify \(2\times 2\) to \(4\).
\[\frac{\frac{\sqrt{2}}{4}}{\frac{4}{5}\times \frac{\sqrt{2}}{2}\times \frac{5}{4}}\]
Cancel \(5\).
\[\frac{\frac{\sqrt{2}}{4}}{4\times \frac{\sqrt{2}}{2}\times \frac{1}{4}}\]
Cancel \(4\).
\[\frac{\frac{\sqrt{2}}{4}}{\frac{\sqrt{2}}{2}}\]
Invert and multiply.
\[\frac{\sqrt{2}}{4}\times \frac{2}{\sqrt{2}}\]
Cancel \(\sqrt{2}\).
\[\frac{1}{4}\times 2\]
Simplify.
\[\frac{2}{4}\]
Simplify.
\[\frac{1}{2}\]
Decimal Form: 0.5
1/2
