Question

$$\frac{ 1 }{ 2 } + \frac{ 1 }{ 3 } \times \frac{ 6 }{ 2 } - \frac{ \frac{ 4 }{ 5 } }{ \frac{ 1 }{ 2 } }$$

Answer

-1/10

Solution


Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{1}{2}+\frac{1\times 6}{3\times 2}-\frac{\frac{4}{5}}{\frac{1}{2}}\]
Simplify  \(1\times 6\)  to  \(6\).
\[\frac{1}{2}+\frac{6}{3\times 2}-\frac{\frac{4}{5}}{\frac{1}{2}}\]
Simplify  \(3\times 2\)  to  \(6\).
\[\frac{1}{2}+\frac{6}{6}-\frac{\frac{4}{5}}{\frac{1}{2}}\]
Cancel \(6\).
\[\frac{1}{2}+1-\frac{\frac{4}{5}}{\frac{1}{2}}\]
Invert and multiply.
\[\frac{1}{2}+1-\frac{4}{5}\times 2\]
Use this rule: \(\frac{a}{b} \times c=\frac{ac}{b}\).
\[\frac{1}{2}+1-\frac{4\times 2}{5}\]
Simplify  \(4\times 2\)  to  \(8\).
\[\frac{1}{2}+1-\frac{8}{5}\]
Simplify.
\[-\frac{1}{10}\]

Decimal Form: -0.1