Question

Use the properties of operations and rules for multiplying and dividing to solve:

(8/9)×(−3/4)÷(1/9)×(−4/5)÷(3/5)


(1 point)

Answer 1

To solve the expression \((8/9) \times (-3/4) \div (1/9) \times (-4/5) \div (3/5)\), we will follow the order of operations (multiplication and division left to right) and simplify as we go.

Let's rewrite the expression for clarity:

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

We can turn the divisions into multiplications by using the reciprocal:

\[
\frac{8}{9} \times \frac{-3}{4} \times \frac{9}{1} \times \frac{-5}{4} \times \frac{5}{3}
\]

Now let's simplify the expression in steps.

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

2. **Next, multiply by \(\frac{9}{1}\):**
\[
\frac{-2}{3} \times \frac{9}{1} = \frac{-2 \times 9}{3 \times 1} = \frac{-18}{3} = -6
\]

3. **Now multiply by \(\frac{-5}{4}\):**
\[
-6 \times \frac{-5}{4} = \frac{-6 \times -5}{1 \times 4} = \frac{30}{4} = \frac{15}{2}
\]

4. **Finally, multiply by \(\frac{5}{3}\):**
\[
\frac{15}{2} \times \frac{5}{3} = \frac{15 \times 5}{2 \times 3} = \frac{75}{6} = \frac{25}{2}
\]

Thus, the final result is

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

So, the solution to the expression is \(\mathbf{\frac{25}{2}}\).