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Solve:

(8/9) x (-3/4) divided by (1/9) x (-4/5) divided by (3/5)

3 answers

To solve the expression \((8/9) \times (-3/4) \div (1/9) \times (-4/5) \div (3/5)\), we'll break it down step by step.

  1. Calculate the first part: \[ (8/9) \times (-3/4) = \frac{8 \times -3}{9 \times 4} = \frac{-24}{36} \] Simplifying \(-24/36\): \[ \frac{-24}{36} = \frac{-2}{3} \]

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

  3. Put it together and perform the first division: Now we have: \[ \frac{-2/3}{-4/45} \] When dividing two fractions, we multiply by the reciprocal: \[ \frac{-2}{3} \div \frac{-4}{45} = \frac{-2}{3} \times \frac{45}{-4} = \frac{-2 \times 45}{3 \times -4} = \frac{90}{12} \] Simplifying \(90/12\): \[ \frac{90}{12} = \frac{15}{2} \]

  4. Now proceed with the final division: Next, we divide this result by \((3/5)\): \[ \frac{15/2}{3/5} = \frac{15}{2} \div \frac{3}{5} = \frac{15}{2} \times \frac{5}{3} = \frac{15 \times 5}{2 \times 3} = \frac{75}{6} \] Simplifying \(75/6\): \[ \frac{75}{6} = \frac{25}{2} \]

So the final answer is: \[ \boxed{\frac{25}{2}} \]

Wrong

Let’s carefully re-evaluate the expression step by step. The expression we need to solve is:

\[ \left(\frac{8}{9} \times \left(-\frac{3}{4}\right)\right) \div \left(\frac{1}{9} \times \left(-\frac{4}{5}\right)\right) \div \left(\frac{3}{5}\right) \]

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

  2. Calculate the second multiplication: \[ \frac{1}{9} \times \left(-\frac{4}{5}\right) = \frac{1 \times -4}{9 \times 5} = \frac{-4}{45} \]

  3. Now let's rewrite the expression using these results: \[ \left(-\frac{2}{3}\right) \div \left(-\frac{4}{45}\right) \]

    Dividing by a fraction is the same as multiplying by its reciprocal: \[ -\frac{2}{3} \times \left(-\frac{45}{4}\right) = \frac{2 \times 45}{3 \times 4} = \frac{90}{12} = \frac{15}{2} \quad (\text{after simplifying}) \]

  4. Now we take this result and divide by \(\frac{3}{5}\): \[ \frac{15}{2} \div \frac{3}{5} \]

    Again, we multiply by the reciprocal: \[ \frac{15}{2} \times \frac{5}{3} = \frac{15 \times 5}{2 \times 3} = \frac{75}{6} \]

    Simplifying \(\frac{75}{6}\): \[ \frac{75}{6} = \frac{25}{2} \quad (\text{after dividing numerator and denominator by 3}) \]

Thus, the final answer is:

\[ \boxed{\frac{25}{2}} \]

It seems the solution derived has been consistent. If there's an error or a different context in which the expression needs to be evaluated, please specify it so that I can assist accurately!