\left(-\frac{3}{5}\right)\times \left(\frac{5}{16}\right)\times \left(\frac{7}{12}\right)\div \left(-\frac{3}{16}\right)\times \left(-\frac{5}{7}\right)

Answer 1

To simplify this expression, we can cancel out any common factors in the numerator and denominator.

Starting with the numerator:
$-\frac{3}{5}\times \frac{5}{16}\times \frac{7}{12} = -\frac{3\cdot 5\cdot 7}{5\cdot 16\cdot 12} = -\frac{105}{960}$

Now let's simplify the denominator:
$-\frac{3}{16}\times -\frac{5}{7}= \frac{3\cdot 5}{16\cdot 7} = \frac{15}{112}$

Finally, we can divide:
$(-\frac{105}{960}) \div \frac{15}{112} = -\frac{105}{960} \times \frac{112}{15}$

To simplify this division, we multiply by the reciprocal:
$-\frac{105}{960} \times \frac{112}{15} = -\frac{105\cdot 112}{960\cdot 15} = -\frac{105\cdot 112}{14400}$

Factoring out a common factor:
$-\frac{105\cdot 112}{14400} = -\frac{105\cdot 112}{2\cdot 7200}$

Simplifying the denominator:
$-\frac{105\cdot 112}{2\cdot 7200} = -\frac{105\cdot 112}{14400} = -\frac{105}{144}\cdot \frac{112}{100} = -\frac{105}{144}\cdot \frac{28}{25}$

Finally, we multiply:
$-\frac{105}{144}\cdot \frac{28}{25} = -\frac{105\cdot 28}{144\cdot 25} = -\frac{2940}{3600}$

So, the simplified expression is $-\frac{2940}{3600}$.