Question

Use the properties of operations and rules for multiplying and dividing to solve: (9)÷(5/4)×(7/9)×(−5)÷(72)

Answer 1

To solve the expression \( (9) \div \left(\frac{5}{4}\right) \times \left(\frac{7}{9}\right) \times (-5) \div (72) \), we can follow the order of operations by simplifying each step clearly.

1. **Dividing by a fraction**: Dividing by a fraction is equivalent to multiplying by its reciprocal.

\[
9 \div \left(\frac{5}{4}\right) = 9 \times \left(\frac{4}{5}\right) = \frac{9 \times 4}{5} = \frac{36}{5}
\]

2. **Now substitute this back into the expression**:

\[
\frac{36}{5} \times \left(\frac{7}{9}\right) \times (-5) \div 72
\]

3. **Multiply the fractions**:

\[
\frac{36}{5} \times \frac{7}{9} = \frac{36 \times 7}{5 \times 9} = \frac{252}{45}
\]

4. **Simplify \( \frac{252}{45} \)**:

Both 252 and 45 can be divided by 9:

\[
\frac{252 \div 9}{45 \div 9} = \frac{28}{5}
\]

5. **Now we multiply by -5**:

\[
\frac{28}{5} \times (-5) = \frac{28 \times -5}{5} = -28
\]

6. **Finally, divide by 72**:

\[
-28 \div 72 = \frac{-28}{72}
\]

7. **Simplify \(\frac{-28}{72}\)**:

Both -28 and 72 can be divided by 4:

\[
\frac{-28 \div 4}{72 \div 4} = \frac{-7}{18}
\]

Thus, the final result of the expression \( (9) \div \left(\frac{5}{4}\right) \times \left(\frac{7}{9}\right) \times (-5) \div (72) \) is:

\[
\boxed{\frac{-7}{18}}
\]