\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)
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 $-\frac{2940}{3600}$.
To simplify this expression step-by-step, we can follow the order of operations (PEMDAS) and apply the rules of multiplying and dividing fractions. Let's start:
Step 1: Simplify the numerator and denominator of each fraction.
- The numerator of the first fraction is -3, and the denominator is 5.
- The numerator of the second fraction is 5, and the denominator is 16.
- The numerator of the third fraction is 7, and the denominator is 12.
- The numerator of the fourth fraction is -3, and the denominator is 16.
- The numerator of the fifth fraction is -5, and the denominator is 7.
Step 2: Multiply the fractions together.
Multiply the numerators and denominators of the three fractions in the numerator, and likewise for the two fractions in the denominator.
The numerator becomes:
-3 * 5 * 7 = -105
The denominator becomes:
5 * 16 * 12 * -3 * -5 * 7 = -100800
Step 3: Simplify the final fraction.
Simplify the fraction by dividing the numerator by the denominator.
The final result is:
-105 / -100800
Step 4: Simplify the fraction further.
We can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).
The GCD of 105 and 100800 is 105.
Simplifying, we get:
-105 / -100800 = 1 / 960
Therefore, the value of the expression is 1/960.
To simplify the given expression, we need to perform the operations in the correct order: multiplication and division from left to right.
Let's start by multiplying the fractions:
\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)
Multiply the numerators together and multiply the denominators together:
\left(\frac{(-3) \times 5 \times 7}{5 \times 16 \times 12}\right)\div \left(\frac{(-3) \times (-5)}{16 \times 7}\right)
Simplify the numerator and denominator:
\left(\frac{-105}{960}\right)\div \left(\frac{15}{112}\right)
Now, let's divide the fractions:
\frac{-105}{960} \div \frac{15}{112}
To divide fractions, we need to multiply by the reciprocal of the second fraction:
\frac{-105}{960} \times \frac{112}{15}
Multiply the numerators together and multiply the denominators together:
\frac{(-105) \times 112}{960 \times 15}
Simplify the numerator and denominator:
\frac{-11760}{14400}
The final answer is:
-\frac{11760}{14400}