se the properties of operations and rules for multiplying and dividing signed numbers to solve:%0D%0A%0D%0A(−4)×(7/5)×(−3/4)÷(7/15)%0D%0A(%0D%0A−%0D%0A4%0D%0A)%0D%0A×%0D%0A(%0D%0A7%0D%0A5%0D%0A)%0D%0A×%0D%0A(%0D%0A−%0D%0A3%0D%0A4%0D%0A)%0D%0A÷%0D%0A(%0D%0A7%0D%0A15%0D%0A)%0D%0A %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A−14775%0D%0A−%0D%0A147%0D%0A75%0D%0Anegative Start Fraction 147 over 75 End Fraction%0D%0A%0D%0A9%0D%0A9%0D%0A%0D%0A14775%0D%0A147%0D%0A75%0D%0AStart Fraction 147 over 75 End Fraction%0D%0A%0D%0A−9

Answer 1

To solve the expression \((-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \div \left(\frac{7}{15}\right)\), follow these steps:

Step 1: Simplifying the Division

First, we can rewrite the division by a fraction as multiplication by its reciprocal: \[ \div \left(\frac{7}{15}\right) = \times \left(\frac{15}{7}\right) \] So the expression becomes: \[ (-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \times \left(\frac{15}{7}\right) \]

Step 2: Rearranging the Multiplication

We can group the terms together: \[ (-4) \times \left(-\frac{3}{4}\right) \times \left(\frac{7}{5}\right) \times \left(\frac{15}{7}\right) \]

Step 3: Calculate the Products Step by Step

Part 1: Multiply the Negative Numbers

\[ (-4) \times \left(-\frac{3}{4}\right) = \frac{4 \times 3}{4} = 3 \]

Part 2: Include Remaining Terms

Now we have: \[ 3 \times \left(\frac{7}{5}\right) \times \left(\frac{15}{7}\right) \]

Step 4: Simplify Further

Now, multiply these fractions: \[ 3 \times \left(\frac{7 \times 15}{5 \times 7}\right) \] Here, the \(7\) in the numerator and denominator cancel out: \[ = 3 \times \left(\frac{15}{5}\right) = 3 \times 3 = 9 \]

Conclusion

The final answer is \(9\).

Thus, the correct response is: 9