Question

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**