Question

Use the properties of operations and rules for multiplying and dividing to solve:

(−2) × (1/5) ÷ (2/3) × (−5/6) ÷ (3/4)

(1 point)
Responses

−1/6
negative Start Fraction 1 over 6 End Fraction

−2/3
negative Start Fraction 2 over 3 End Fraction

1/6
Start Fraction 1 over 6 End Fraction

2/3

Answer 1

To solve the expression \( (-2) \times \left(\frac{1}{5}\right) \div \left(\frac{2}{3}\right) \times \left(-\frac{5}{6}\right) \div \left(\frac{3}{4}\right) \), we can follow the order of operations, handling multiplication and division from left to right.

1. Start with the first operation:
\[
(-2) \times \left(\frac{1}{5}\right) = -\frac{2}{5}.
\]

2. Next, divide by \(\left(\frac{2}{3}\right)\):
\[
-\frac{2}{5} \div \left(\frac{2}{3}\right) = -\frac{2}{5} \times \left(\frac{3}{2}\right) = -\frac{2 \times 3}{5 \times 2} = -\frac{6}{10} = -\frac{3}{5}.
\]

3. Multiply by \(\left(-\frac{5}{6}\right)\):
\[
-\frac{3}{5} \times \left(-\frac{5}{6}\right) = \frac{3 \times 5}{5 \times 6} = \frac{15}{30} = \frac{1}{2}.
\]

4. Finally, divide by \(\left(\frac{3}{4}\right)\):
\[
\frac{1}{2} \div \left(\frac{3}{4}\right) = \frac{1}{2} \times \left(\frac{4}{3}\right) = \frac{1 \times 4}{2 \times 3} = \frac{4}{6} = \frac{2}{3}.
\]

Thus, the final result is:

\[
\frac{2}{3}.
\]

So the answer is \( 2/3 \) (which corresponds to the option provided).