6 of 156 of 15 Items

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

9
9

-9
-9

−147/75

147/75

Answer 1

To solve the expression \((−4) ×(7/5) ×(−3/4)÷(7/15)\), we can break it down step by step.

1. Multiply the first two terms: \[ (−4) × (7/5) = -\frac{28}{5} \]

2. Now, multiply by \(-3/4\): \[ \left(-\frac{28}{5}\right) × \left(-\frac{3}{4}\right) = \frac{28 \times 3}{5 \times 4} = \frac{84}{20} = \frac{21}{5} \]

3. Now, divide by \((7/15)\): To divide by a fraction, we multiply by its reciprocal: \[ \frac{21}{5} ÷ \left(\frac{7}{15}\right) = \frac{21}{5} × \left(\frac{15}{7}\right) \]

4. Multiply the fractions: \[ \frac{21 × 15}{5 × 7} = \frac{315}{35} = 9 \]

So the final result is \(9\).

The correct response is: 9