Question

Use the properties of operation and rules 4 multiplying and dividing to solve
( 9) divide ( 5/4 ) x ( 7/9 ) x ( -5 ) divided by ( 7/2)

-8
8
-1,225/8
1,225/8

Answer 1

To simplify the expression \((9) \div \left(\frac{5}{4}\right) \times \left(\frac{7}{9}\right) \times (-5) \div \left(\frac{7}{2}\right)\), we will follow the order of operations and apply the properties of multiplication and division.

First, we can rewrite the expression:
\[
9 \div \left(\frac{5}{4}\right) \times \left(\frac{7}{9}\right) \times (-5) \div \left(\frac{7}{2}\right)
\]

We'll start by dealing with the divisions. Dividing by a fraction is equal to multiplying by its reciprocal. Thus, we can rewrite \(\div \left(\frac{5}{4}\right)\) and \(\div \left(\frac{7}{2}\right)\) as follows:
\[
9 \times \left(\frac{4}{5}\right) \times \left(\frac{7}{9}\right) \times (-5) \times \left(\frac{2}{7}\right)
\]

Now, let's multiply these fractions step-by-step.

1. **Combine \(9\) and \(\left(\frac{4}{5}\right)\)**:
\[
9 \times \left(\frac{4}{5}\right) = \frac{36}{5}
\]

2. **Multiply by \(\left(\frac{7}{9}\right)\)**:
\[
\frac{36}{5} \times \left(\frac{7}{9}\right) = \frac{36 \times 7}{5 \times 9} = \frac{252}{45} = \frac{28}{5} \text{ (after simplifying)}
\]

3. **Now multiply by \(-5\)**:
\[
\frac{28}{5} \times (-5) = \frac{28 \times (-5)}{5} = -28
\]

4. **Finally, multiply by \(\left(\frac{2}{7}\right)\)**:
\[
-28 \times \left(\frac{2}{7}\right) = \frac{-28 \times 2}{7} = -\frac{56}{7} = -8
\]

Thus, the final answer from the calculation is \(-8\).

The answer is:
\[
\boxed{-8}
\]