Question

Use the properties of operations and rules for multiplying and dividing to solve:
(8/9) x (-3/4) divided by (1/9) x (-4/5) divided by (3/5)

Answer 1

It says its wrong.

Answer 2

Let's break down the expression step by step. We need to solve the following:

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

First, calculate the numerator:

\[
(8/9) \times (-3/4) = \frac{8 \times -3}{9 \times 4} = \frac{-24}{36}
\]

We can simplify \(\frac{-24}{36}\):

\[
-24 \div 12 = -2 \quad \text{and} \quad 36 \div 12 = 3
\]

So,

\[
\frac{-24}{36} = \frac{-2}{3}
\]

Now calculate the denominator:

\[
(1/9) \times (-4/5) = \frac{1 \times -4}{9 \times 5} = \frac{-4}{45}
\]

Now we substitute these into the expression:

\[
\frac{-2/3}{-4/45}
\]

Dividing a fraction by another fraction involves multiplying by the reciprocal:

\[
\frac{-2}{3} \div \frac{-4}{45} = \frac{-2}{3} \times \frac{45}{-4}
\]

Cancelling the negatives gives:

\[
\frac{2}{3} \times \frac{45}{4}
\]

Now we multiply the fractions:

\[
\frac{2 \times 45}{3 \times 4} = \frac{90}{12}
\]

We can simplify \(\frac{90}{12}\):

\[
90 \div 6 = 15 \quad \text{and} \quad 12 \div 6 = 2
\]

So,

\[
\frac{90}{12} = \frac{15}{2}
\]

We still need to divide this by \(\frac{3}{5}\):

\[
\frac{15}{2} \div \frac{3}{5} = \frac{15}{2} \times \frac{5}{3}
\]

Multiplying the fractions gives:

\[
\frac{15 \times 5}{2 \times 3} = \frac{75}{6}
\]

We can simplify this:

\[
75 \div 3 = 25 \quad \text{and} \quad 6 \div 3 = 2
\]

Thus,

\[
\frac{75}{6} = \frac{25}{2}
\]

In conclusion, the answer is:

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

or as a mixed number, \(12 \frac{1}{2}\).

Answer 3

I apologize for any confusion. Let's carefully go through the calculation again step by step.

The original expression we need to solve is:

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

### Step 1: Calculate the numerator

Calculate \((8/9) \times (-3/4)\):

\[
\frac{8}{9} \times \frac{-3}{4} = \frac{8 \times -3}{9 \times 4} = \frac{-24}{36}
\]

Now simplify \(\frac{-24}{36}\):

\[
\frac{-24 \div 12}{36 \div 12} = \frac{-2}{3}
\]

### Step 2: Calculate the denominator

Next, calculate \((1/9) \times (-4/5)\):

\[
\frac{1}{9} \times \frac{-4}{5} = \frac{1 \times -4}{9 \times 5} = \frac{-4}{45}
\]

### Step 3: Putting it together

Now substitute these into the fraction:

\[
\frac{-2/3}{-4/45}
\]

### Step 4: Divide the fractions

To divide these fractions, multiply by the reciprocal of the denominator:

\[
\frac{-2}{3} \div \frac{-4}{45} = \frac{-2}{3} \times \frac{45}{-4}
\]

The negative signs cancel out:

\[
\frac{2}{3} \times \frac{45}{4} = \frac{2 \times 45}{3 \times 4} = \frac{90}{12}
\]

### Step 5: Simplify \(\frac{90}{12}\)

Now simplify \(\frac{90}{12}\):

\[
\frac{90 \div 6}{12 \div 6} = \frac{15}{2}
\]

### Step 6: Now we need to divide by \(\frac{3}{5}\)

\(\frac{15}{2} \div \frac{3}{5} = \frac{15}{2} \times \frac{5}{3}\)

\[
= \frac{15 \times 5}{2 \times 3} = \frac{75}{6}
\]

### Step 7: Simplify \(\frac{75}{6}\)

Now simplify \(\frac{75}{6}\):

\[
\frac{75 \div 3}{6 \div 3} = \frac{25}{2}
\]

### Final Answer

Thus, the final answer is:

\[
\frac{25}{2} \quad \text{(or } 12.5 \text{ as a decimal)}
\]

If there was a misunderstanding of your question or a different expression you wanted to solve, please clarify, and I would be happy to assist further!