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
Start Fraction 2 over 3 End Fraction

−16
negative Start Fraction 1 over 6 End Fraction

−23
negative Start Fraction 2 over 3 End Fraction

16

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. Convert the division by a fraction into multiplication by its 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, we can multiply all these factors together:

\[
= (-2) \times \left(\frac{1}{5}\right) \times \left(\frac{3}{2}\right) \times \left(-\frac{5}{6}\right) \times \left(\frac{4}{3}\right)
\]

3. Combine the numerical coefficients and fractions:

\[
= \frac{(-2) \times 1 \times 3 \times (-5) \times 4}{5 \times 2 \times 6 \times 3}
\]

4. Calculate the numerator:

\[
= (-2) \times (-5) \times 4 \times 3 = 2 \times 5 \times 4 \times 3 = 120
\]

5. Calculate the denominator:

\[
= 5 \times 2 \times 6 \times 3 = 180
\]

6. So, we have:

\[
= \frac{120}{180}
\]

7. Simplify the fraction:

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

Thus, the final answer is \(\frac{2}{3}\).

From the options provided, the correct response is:

**Start Fraction 2 over 3 End Fraction**.