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

−23
negative Start Fraction 2 over 3 End Fraction

−16
negative Start Fraction 1 over 6 End Fraction

23
Start Fraction 2 over 3 End Fraction

16
Start Fraction 1 over 6 End Fraction
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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 and simplify step by step.

1. Rewrite the division as multiplication by the reciprocal:
\[
(-2) \times \left(\frac{1}{5}\right) \times \left(\frac{3}{2}\right) \times \left(-\frac{5}{6}\right) \times \left(\frac{4}{3}\right)
\]

2. Now group and multiply together:
\[
(-2) \times (-\frac{5}{6}) \times \left(\frac{1}{5}\right) \times \left(\frac{3}{2}\right) \times \left(\frac{4}{3}\right)
\]

3. First, compute the multiplication of the first two terms:
\[
(-2) \times (-\frac{5}{6}) = \frac{10}{6} = \frac{5}{3}
\]

4. Now multiply this result with \(\left(\frac{1}{5}\right)\):
\[
\frac{5}{3} \times \frac{1}{5} = \frac{5 \times 1}{3 \times 5} = \frac{1}{3}
\]

5. Multiply this with \(\left(\frac{3}{2}\right)\):
\[
\frac{1}{3} \times \frac{3}{2} = \frac{1 \times 3}{3 \times 2} = \frac{3}{6} = \frac{1}{2}
\]

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

Thus, the final answer is:
\[
\boxed{\frac{2}{3}}
\]