Question

$$(1997 \frac{ 1 }{ 5 } -1996 \frac{ 1 }{ 6 } ) \times 1 \frac{ 29 }{ 31 }$$

Answer

29029/465

Solution


Simplify  \(1997\times \frac{1}{5}\)  to  \(\frac{1997}{5}\).
\[(\frac{1997}{5}-1996\times \frac{1}{6})\times 1\times \frac{29}{31}\]
Simplify  \(1996\times \frac{1}{6}\)  to  \(\frac{1996}{6}\).
\[(\frac{1997}{5}-\frac{1996}{6})\times 1\times \frac{29}{31}\]
Simplify  \(\frac{1996}{6}\)  to  \(\frac{998}{3}\).
\[(\frac{1997}{5}-\frac{998}{3})\times 1\times \frac{29}{31}\]
Simplify  \(\frac{1997}{5}-\frac{998}{3}\)  to  \(\frac{1001}{15}\).
\[\frac{1001}{15}\times 1\times \frac{29}{31}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{1001\times 1\times 29}{15\times 31}\]
Simplify  \(1001\times 1\)  to  \(1001\).
\[\frac{1001\times 29}{15\times 31}\]
Simplify  \(1001\times 29\)  to  \(29029\).
\[\frac{29029}{15\times 31}\]
Simplify  \(15\times 31\)  to  \(465\).
\[\frac{29029}{465}\]

Decimal Form: 62.427957