Question

8/9 times -3/4 divided by 1/9 times -4/5 divided by 3/5

Answer 1

To solve the expression \(\frac{8}{9} \times \left(-\frac{3}{4}\right) \div \left(\frac{1}{9} \times \left(-\frac{4}{5}\right) \div \frac{3}{5}\right)\), we will follow the operations step by step.

1. **Calculate the numerator**:
\[
\frac{8}{9} \times \left(-\frac{3}{4}\right) = -\frac{8 \times 3}{9 \times 4} = -\frac{24}{36} = -\frac{2}{3} \quad \text{(after simplifying)}
\]

2. **Calculate the denominator**:
- First calculate \(\frac{1}{9} \times \left(-\frac{4}{5}\right)\):
\[
\frac{1}{9} \times \left(-\frac{4}{5}\right) = -\frac{4}{45}
\]

- Now divide this by \(\frac{3}{5}\):
\[
-\frac{4}{45} \div \frac{3}{5} = -\frac{4}{45} \times \frac{5}{3} = -\frac{20}{135} = -\frac{4}{27} \quad \text{(after simplifying)}
\]

3. **Now we can combine our results**:
\[
-\frac{2}{3} \div \left(-\frac{4}{27}\right) = -\frac{2}{3} \times -\frac{27}{4} = \frac{2 \times 27}{3 \times 4} = \frac{54}{12} = \frac{9}{2} \quad \text{(after simplifying)}
\]

Thus, the final result of the entire expression is:
\[
\boxed{\frac{9}{2}}
\]