Question

$$\frac{ 2 }{ 5 } \times - \frac{ 3 }{ 7 } - \frac{ 1 }{ 14 } - \frac{ 3 }{ 7 } \times \frac{ 3 }{ 5 }$$

Answer

-1/2

Solution


Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{2\times -3}{5\times 7}-\frac{1}{14}-\frac{3}{7}\times \frac{3}{5}\]
Simplify  \(2\times -3\)  to  \(-6\).
\[\frac{-6}{5\times 7}-\frac{1}{14}-\frac{3}{7}\times \frac{3}{5}\]
Simplify  \(5\times 7\)  to  \(35\).
\[\frac{-6}{35}-\frac{1}{14}-\frac{3}{7}\times \frac{3}{5}\]
Move the negative sign to the left.
\[-\frac{6}{35}-\frac{1}{14}-\frac{3}{7}\times \frac{3}{5}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[-\frac{6}{35}-\frac{1}{14}-\frac{3\times 3}{7\times 5}\]
Simplify  \(3\times 3\)  to  \(9\).
\[-\frac{6}{35}-\frac{1}{14}-\frac{9}{7\times 5}\]
Simplify  \(7\times 5\)  to  \(35\).
\[-\frac{6}{35}-\frac{1}{14}-\frac{9}{35}\]
Simplify.
\[-\frac{35}{70}\]
Simplify  \(\frac{35}{70}\)  to  \(\frac{1}{2}\).
\[-\frac{1}{2}\]

Decimal Form: -0.5