Question

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

(−3/5)×(5/16)×(71/2)÷(−3/16)×(−5/7)


(1 point)

Answer 1

To solve the expression \((−3/5)×(5/16)×(71/2)÷(−3/16)×(−5/7)\), we can follow the order of operations and apply the properties of multiplication and division.

First, rewrite the division as multiplication by the reciprocal:

\[
(−3/5) × (5/16) × (71/2) × (−16/3) × (−7/5)
\]

Now, we can simplify step-by-step:

1. **Multiply \( (−3/5) \) by \( (5/16) \)**:
\[
(−3/5) × (5/16) = −3/16
\]

2. **Now the expression is**:
\[
(−3/16) × (71/2) × (−16/3) × (−7/5)
\]

3. **Multiply \( (−3/16) \) by \( (−16/3) \)**:
\[
(−3/16) × (−16/3) = \frac{(-3)(-16)}{(16)(-3)} = 1
\]

4. **Now we have**:
\[
1 × (71/2) × (−7/5)
\]
which simplifies to:
\[
(71/2) × (−7/5)
\]

5. **Multiply \( (71/2) \) by \( (−7/5) \)**:
\[
(71/2) × (−7/5) = \frac{(71)(-7)}{(2)(5)} = \frac{-497}{10}
\]

Thus, the final value of the expression is:

\[
\boxed{-\frac{497}{10}}
\]