Question

$$\frac{ 71 }{ 3 } - \frac{ 21 }{ 4 } ( \frac{ 21 }{ 5 } \times \frac{ 3 }{ 4 } )$$

Answer

1711/240

Solution


Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{71}{3}-\frac{21}{4}\times \frac{21\times 3}{5\times 4}\]
Simplify  \(21\times 3\)  to  \(63\).
\[\frac{71}{3}-\frac{21}{4}\times \frac{63}{5\times 4}\]
Simplify  \(5\times 4\)  to  \(20\).
\[\frac{71}{3}-\frac{21}{4}\times \frac{63}{20}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{71}{3}-\frac{21\times 63}{4\times 20}\]
Simplify  \(21\times 63\)  to  \(1323\).
\[\frac{71}{3}-\frac{1323}{4\times 20}\]
Simplify  \(4\times 20\)  to  \(80\).
\[\frac{71}{3}-\frac{1323}{80}\]
Simplify.
\[\frac{1711}{240}\]

Decimal Form: 7.129167