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 Start Fraction 1 over 6 End Fraction −2/3 negative Start Fraction 2 over 3 End Fraction −1/6 negative Start Fraction 1 over 6 End Fraction 2/3

Answer 1

To solve the expression \((−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)\), we will follow the order of operations and also simplify as we go along.

1. First, we need to convert the divisions into multiplications by multiplying by the reciprocal:

\[
(−2) × (1/5) × \left(\frac{3}{2}\right) × (−5/6) × \left(\frac{4}{3}\right)
\]

2. Now, we can group the multiplication terms:

\[
= (−2) × (1/5) × (3/2) × (−5/6) × (4/3)
\]

3. Let’s multiply the fractions step by step. Start with \((-2) × (1/5)\):

\[
= -\frac{2}{5}
\]

4. Next, multiply by \(\frac{3}{2}\):

\[
-\frac{2}{5} × \frac{3}{2} = -\frac{6}{10} = -\frac{3}{5}
\]

5. Now, multiply by \((-5/6)\):

\[
-\frac{3}{5} × \left(-\frac{5}{6}\right) = \frac{15}{30} = \frac{1}{2}
\]

6. Finally, multiply by \(\frac{4}{3}\):

\[
\frac{1}{2} × \frac{4}{3} = \frac{4}{6} = \frac{2}{3}
\]

The final answer is:

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

Thus, the solution to the expression is \( \frac{2}{3} \).