Question

Use the properties of operations and rules for multiplying and dividing signed numbers to solve: (−4)×(7/5)×(−3/4)÷(7/15) (1 point)

Answer 1

To solve the expression \((-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \div \left(\frac{7}{15}\right)\), we will follow the order of operations and handle the multiplication and division involving signed numbers.

1. **Multiply the first two numbers:**
\[
(-4) \times \left(\frac{7}{5}\right) = -\frac{28}{5}
\]

2. **Now multiply the result by \(-\frac{3}{4}\):**
\[
-\frac{28}{5} \times \left(-\frac{3}{4}\right) = \frac{28 \times 3}{5 \times 4} = \frac{84}{20} = \frac{21}{5} \quad \text{(since both negatives cancel out)}
\]

3. **Now divide the result by \(\frac{7}{15}\):**
\[
\frac{21}{5} \div \left(\frac{7}{15}\right) = \frac{21}{5} \times \left(\frac{15}{7}\right)
\]

Now multiply:
\[
\frac{21 \times 15}{5 \times 7} = \frac{315}{35} = 9
\]

Thus, the final result of the expression \((-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \div \left(\frac{7}{15}\right)\) is:
\[
\boxed{9}
\]