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

2/3
Start Fraction 2 over 3 End Fraction

−1/6
negative Start Fraction 1 over 6 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 will follow the order of operations, performing multiplications and divisions from left to right.

1. **First, calculate** \((-2) \times \left(\frac{1}{5}\right)\):
\[
-2 \times \frac{1}{5} = -\frac{2}{5}.
\]

2. **Next, divide** \(-\frac{2}{5} \div \left(\frac{2}{3}\right)\):
Dividing by a fraction is the same as multiplying by its reciprocal:
\[
-\frac{2}{5} \div \frac{2}{3} = -\frac{2}{5} \times \frac{3}{2} = -\frac{2 \times 3}{5 \times 2} = -\frac{6}{10} = -\frac{3}{5}.
\]

3. **Then, multiply** \(-\frac{3}{5} \times \left(-\frac{5}{6}\right)\):
Since multiplying two negatives results in a positive:
\[
-\frac{3}{5} \times -\frac{5}{6} = \frac{3 \times 5}{5 \times 6} = \frac{15}{30} = \frac{1}{2}.
\]

4. **Finally, divide** \(\frac{1}{2} \div \left(\frac{3}{4}\right)\):
Again, dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \times \frac{4}{3} = \frac{1 \times 4}{2 \times 3} = \frac{4}{6} = \frac{2}{3}.
\]

Thus, the final answer is

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

So the correct response is:

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