Question

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

(9) ÷ (5/4) × (7/9) × (−5) ÷ (7/2)

(1 point)
Responses

1,225/8
Start Fraction 1,225 over 8 End Fraction

−8
negative 8

-8

8

−1,225/8
negative Start Fraction 1,225 over 8 End Fraction

Answer 1

To solve 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 simplify step by step.

1. **Rewrite the expression**:
\[
9 \div \frac{5}{4} \times \frac{7}{9} \times (-5) \div \frac{7}{2}
\]

2. **Convert division by a fraction to multiplication**:
\[
9 \times \frac{4}{5} \times \frac{7}{9} \times (-5) \times \frac{2}{7}
\]

3. **Rearrange the multiplication**:
\[
(9 \times \frac{4}{5} \times \frac{7}{9} \times (-5) \times \frac{2}{7})
\]

4. **Cancel out where possible**:
- The \( 9 \) from the first term and the \( \frac{7}{9} \) will cancel:
\[
= \frac{4}{5} \times (-5) \times 2
\]

5. **Multiply**:
- \( -5 \times \frac{4}{5} = -4 \)
- Then multiply by \( 2 \):
\[
-4 \times 2 = -8
\]

Thus, the final answer is:
\[
\boxed{-8}
\]