Question

Use the properties of operations and rules for multiplying and dividing to solve: (−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7).

Answer 1

We will solve the expression \((-3/5) \times (5/16) \times (7/12) \div (-3/16) \times (-5/7)\) step-by-step.

First, we can rewrite the division as multiplication by the reciprocal:

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

Next, let's focus on the multiplication of all the fractions in the expression:

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

Now we can combine the fractions:

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

Now we can simplify the expression:

1. Note that the \(-3\) in the numerator and the denominator cancels out.
2. The \(5\) in the numerator and denominator cancels out too.
3. There are two \(-16\) in the numerator which can be adjusted to have one as positive after the cancellation.

Thus, we have:

\[
= \frac{(7) \times (-16) \times (-7)}{16 \times 12}
\]

Now we can simplify \((-16) \times (-7)\):

\[
= 16 \times 7 = 112
\]

So, the expression simplifies to:

\[
= \frac{112}{16 \times 12}
\]

Now let's compute \(16 \times 12 = 192\):

So we now have:

\[
= \frac{112}{192}
\]

Next, let's simplify \(\frac{112}{192}\) by finding the greatest common divisor (GCD) of 112 and 192, which is 16:

\[
= \frac{112 \div 16}{192 \div 16} = \frac{7}{12}
\]

Thus, the final answer is:

\[
\boxed{\frac{7}{12}}
\]