Question

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

(−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7)


(1 point)

Answer 1

wrong

Answer 2

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

1. Convert the division into multiplication by taking the reciprocal of the divisor:

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

2. Now, we can combine all the fractions:

\[
= \frac{-3 \times 5 \times 7 \times -16 \times -5}{5 \times 16 \times 12 \times -3 \times 7}
\]

3. Let's simplify step by step:

- The numerator is \(-3 \times 5 \times 7 \times -16 \times -5\).
- The denominator is \(5 \times 16 \times 12 \times -3 \times 7\).

4. We can start canceling terms from the numerator and denominator:

- The \(-3\) in the numerator and denominator cancels out.
- The \(5\) in the numerator and denominator cancels out.
- The \(7\) in the numerator and denominator cancels out.

After canceling, we simplify:

\[
= \frac{(-16) \times (-5)}{16 \times 12}
\]

5. This simplifies to:

\[
= \frac{80}{192}
\]

6. Now we simplify \(\frac{80}{192}\):

The greatest common divisor of 80 and 192 is 16.

Dividing the numerator and the denominator by 16 gives us:

\[
= \frac{5}{12}
\]

Thus, the final answer is:

\[
\boxed{\frac{5}{12}}
\]