Question

use the properties of operations and rules for multiplying and dividing to solve :
\left(8\backslash9\right)\times\left(-\ 3\backslash4\right)\div\left(1\backslash9\right)\times\left(-\ 4\backslash5\right)\div\left(3\backslash5\right)

Answer 1

To solve the expression \((8 \backslash 9) \times (-3 \backslash 4) \div (1 \backslash 9) \times (-4 \backslash 5) \div (3 \backslash 5)\), we first need to clarify what you mean by the symbol "\backslash." If we assume it denotes a fraction, we will rewrite it using the division notation.

Thus, we can translate the expression into fractions as follows:

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

Now, we'll perform the calculations step by step:

1. Calculate the first multiplication:

\[
\frac{8}{9} \times \left(-\frac{3}{4}\right) = -\frac{8 \times 3}{9 \times 4} = -\frac{24}{36} = -\frac{2}{3}
\]

2. Now we will divide this result by \(\frac{1}{9}\). Dividing by a fraction is the same as multiplying by its reciprocal:

\[
-\frac{2}{3} \div \frac{1}{9} = -\frac{2}{3} \times 9 = -2 \times 3 = -6
\]

3. Next, we will multiply this result by \(-\frac{4}{5}\):

\[
-6 \times \left(-\frac{4}{5}\right) = \frac{24}{5}
\]

4. Finally, we will divide this result by \(\frac{3}{5}\):

\[
\frac{24}{5} \div \frac{3}{5} = \frac{24}{5} \times \frac{5}{3} = \frac{24 \times 5}{5 \times 3} = \frac{24}{3} = 8
\]

Thus, the final answer is:

\[
\boxed{8}
\]