Question

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)
Responses

14775
Start Fraction 147 over 75 End Fraction

−9
negative 9

9
9

−14775

Answer 1

To solve \((-4) \times \left(\frac{7}{5}\right) \times \left(-\frac{3}{4}\right) \div \left(\frac{7}{15}\right)\), we can start by handling the multiplication first.

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

2. **Next, multiply by \(-\frac{3}{4}\)**:
\[
\frac{-28}{5} \times \left(-\frac{3}{4}\right) = \frac{-28 \times -3}{5 \times 4} = \frac{84}{20}
\]

3. **Now, simplify \(\frac{84}{20}\)**:
The GCD (Greatest Common Divisor) of 84 and 20 is 4.
\[
\frac{84 \div 4}{20 \div 4} = \frac{21}{5}
\]

4. **Now we need to divide by \(\frac{7}{15}\)**. Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{21}{5} \div \left(\frac{7}{15}\right) = \frac{21}{5} \times \left(\frac{15}{7}\right)
\]

5. **Multiply the fractions**:
\[
\frac{21 \times 15}{5 \times 7} = \frac{315}{35}
\]

6. **Now simplify \(\frac{315}{35}\)**:
The GCD of 315 and 35 is 105.
\[
\frac{315 \div 105}{35 \div 105} = \frac{63}{7} = 9
\]

Therefore, the final answer is:

\[
\boxed{9}
\]