Use the properties of operations and rules for multiplying and dividing to solve:

Question

(−3/5) × (5/16) × (7/12) ÷ (−3/16) × (−5/7)


(1 point)
_________

Answer 1

To solve the expression $(-\frac{3}{5})\times (\frac{5}{16})\times (\frac{7}{12})÷(-\frac{3}{16})\times (-\frac{5}{7})$, we can simplify step by step.

1. Rewrite the division as multiplication by the reciprocal:
   The division of fractions can be rewritten by taking the reciprocal of the divisor: $$÷(-\frac{3}{16})\text{becomes}\times (-\frac{16}{3})$$ So the expression now looks like this: $$(-\frac{3}{5})\times (\frac{5}{16})\times (\frac{7}{12})\times (-\frac{16}{3})\times (-\frac{5}{7})$$

2. Combine the factors:
   We can multiply all the fractions together: $$(-\frac{3}{5})\times (\frac{5}{16})\times (\frac{7}{12})\times (-\frac{16}{3})\times (-\frac{5}{7})=\frac{(-3)\times 5\times 7\times (-16)\times (-5)}{5\times 16\times 12\times 3\times 7}$$

3. Calculating the numerator and denominator:

   • Numerator:
     $(-3)\times 5\times 7\times (-16)\times (-5)$ equals: $$3\times 5\times 7\times 16\times 5=3\times 5^2\times 7\times 16=3\times 25\times 7\times 16$$
   • Denominator:
     $5\times 16\times 12\times 3\times 7$

4. Cancelling out common factors:
   We notice:

   • The $5$ in the numerator and denominator cancels.
   • The $7$ in the numerator and denominator cancels.
   • The $3$ cancels with the multiple in the denominator.
   • The $16$ cancels with the multiple in the denominator.

   After all cancellations, we can look at the simple ratios remaining.

5. Final multiplication:
   $\frac{3\times 5\times 7\times 16\times 5}{5\times 16\times 12\times 3\times 7}$ reduces down to a simple multiplication of whatever remains.

Now calculate directly: Using remaining terms leads us to: $$\frac{1}{12}$$

So, the final answer is: $$\frac{1}{12}$$