Question

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

(9)÷(5/4)×(7/9)×(−5)÷(7/2)

Answer 1

To solve the expression \((9) \div (5/4) \times (7/9) \times (-5) \div (7/2)\), we will follow the order of operations and use the properties of fractions and division.

1. **Rewrite the division as multiplication by the reciprocal**:
\[
9 \div (5/4) = 9 \times (4/5)
\]
\[
-5 \div (7/2) = -5 \times (2/7)
\]

So the expression becomes:
\[
(9 \times (4/5)) \times (7/9) \times (-5 \times (2/7))
\]

2. **Combine the expression**:
\[
(9 \times (4/5)) \times (7/9) \times (-5) \times (2/7)
\]

We can now simplify this step by step.

3. **Multiply \(9\) and \((7/9)\)**:
\[
9 \times (7/9) = 7
\]

Now the expression simplifies to:
\[
(7 \times (4/5)) \times (-5) \times (2/7)
\]

4. **Multiply \(7\) by \((4/5)\)**:
\[
7 \times (4/5) = \frac{28}{5}
\]

The expression now looks like:
\[
\left(\frac{28}{5}\right) \times (-5) \times (2/7)
\]

5. **Multiply \(\frac{28}{5}\) and \(-5\)**:
\[
\frac{28}{5} \times (-5) = -\frac{28 \times 5}{5} = -28
\]

Thus, our expression now is:
\[
-28 \times (2/7)
\]

6. **Multiply \(-28\) by \((2/7)\)**:
\[
-28 \times (2/7) = -\frac{28 \times 2}{7} = -\frac{56}{7} = -8
\]

So, the final result is:
\[
\boxed{-8}
\]