Question

what is 8/9 times -3/4 divided 1/9 times -4/5 divided 3/5

Answer 1

To solve the expression \((\frac{8}{9} \times \frac{-3}{4}) \div (\frac{1}{9} \times \frac{-4}{5} \div \frac{3}{5})\), we will break it down step by step.

1. **Calculate \(\frac{8}{9} \times \frac{-3}{4}\)**:
\[
\frac{8}{9} \times \frac{-3}{4} = \frac{8 \times -3}{9 \times 4} = \frac{-24}{36} = \frac{-2}{3}
\]

2. **Calculate \(\frac{1}{9} \times \frac{-4}{5}\)**:
\[
\frac{1}{9} \times \frac{-4}{5} = \frac{1 \times -4}{9 \times 5} = \frac{-4}{45}
\]

3. **Now divide \(\frac{-4}{45}\) by \(\frac{3}{5}\)**:
When dividing by a fraction, we multiply by its reciprocal:
\[
\frac{-4}{45} \div \frac{3}{5} = \frac{-4}{45} \times \frac{5}{3} = \frac{-4 \times 5}{45 \times 3} = \frac{-20}{135}
\]
We can simplify \(\frac{-20}{135}\):
\[
\frac{-20}{135} = \frac{-4}{27} \quad \text{(dividing the numerator and denominator by 5)}
\]

4. **Now we have \(\frac{-2}{3} \div \frac{-4}{27}\)**:
Again, we multiply by the reciprocal:
\[
\frac{-2}{3} \div \frac{-4}{27} = \frac{-2}{3} \times \frac{27}{-4} = \frac{-2 \times 27}{3 \times -4} = \frac{54}{12}
\]
We can simplify \(\frac{54}{12}\):
\[
\frac{54}{12} = \frac{9}{2} \quad \text{(dividing the numerator and denominator by 6)}
\]

Thus, the final answer is:
\[
\frac{9}{2}
\]