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

−1,2258
negative Start Fraction 1,225 over 8 End Fraction

−8
negative 8

8
8

1,2258

Answer 1

To solve the expression \((9)÷(5/4)×(7/9)×(−5)÷(7/2)\), we can follow the order of operations and simplify step by step.

1. **Convert division into multiplication** by multiplying by the reciprocal:
\[
9 \div \left(\frac{5}{4}\right) = 9 \times \left(\frac{4}{5}\right) = \frac{36}{5}
\]
Thus, the expression becomes:
\[
\frac{36}{5} \times \left(\frac{7}{9}\right) \times (-5) \div \left(\frac{7}{2}\right)
\]
Next, we also rewrite the division by \(\frac{7}{2}\) as multiplication by its reciprocal:
\[
\div \left(\frac{7}{2}\right) = \times \left(\frac{2}{7}\right)
\]
Therefore, the expression now looks like:
\[
\frac{36}{5} \times \left(\frac{7}{9}\right) \times (-5) \times \left(\frac{2}{7}\right)
\]

2. **Simplify the expression**:
Start by multiplying \(\frac{36}{5}\) and \(\frac{7}{9}\):
\[
\frac{36}{5} \times \frac{7}{9} = \frac{36 \cdot 7}{5 \cdot 9} = \frac{252}{45}
\]

3. **Multiply by \(-5\)**:
\[
\frac{252}{45} \times (-5) = \frac{252 \times (-5)}{45} = \frac{-1260}{45}
\]

4. **Simplify \(\frac{-1260}{45}\)**:
Divide both the numerator and denominator by 45:
\[
-1260 \div 45 = -28
\]
(since \(1260\div 45 = 28\))

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

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