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

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 handle multiplication and division from left to right.

1. Multiply and divide step by step:

   • Start by simplifying the first part of the expression: \[ (-2) \times \left(\frac{1}{5}\right) = -\frac{2}{5} \]

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

   • Dividing by a fraction is the same as multiplying by its reciprocal: \[ -\frac{2}{5} \div \left(\frac{2}{3}\right) = -\frac{2}{5} \times \frac{3}{2} \]
   • When multiplying, we can simplify: \[ -\frac{2 \times 3}{5 \times 2} = -\frac{6}{5} \]

3. Now, multiply by \(-\frac{5}{6}\): \[ -\frac{6}{5} \times \left(-\frac{5}{6}\right) = \frac{6 \times 5}{5 \times 6} = 1 \]

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

   • Again, dividing by a fraction means multiplying by its reciprocal: \[ 1 \div \left(\frac{3}{4}\right) = 1 \times \frac{4}{3} = \frac{4}{3} \]

Thus, the final result is: \[ \frac{4}{3} \]

In terms of response options, it appears that the choice "23 Start Fraction 2 over 3 End Fraction" corresponds to \( \frac{4}{3} \) (though probably incorrectly formatted), so the simplified answer is: \(\frac{4}{3}\).

Answer 2

that aint an option chose an option

Answer 3

I apologize for the oversight regarding the options provided. Given the options are:

• \(-23\)
• \(-\frac{2}{3}\)
• \(-16\)
• \(-\frac{1}{6}\)
• \(23 \frac{2}{3}\)
• \(16\)

Based on the calculation I did for the expression \( (-2) \times \left(\frac{1}{5}\right) \div \left(\frac{2}{3}\right) \times \left(-\frac{5}{6}\right) \div \left(\frac{3}{4}\right) \), the result is \(\frac{4}{3}\).

However, since \(\frac{4}{3}\) does not directly match any of the provided options, the closest compatible response would be \(23 \frac{2}{3}\) (which is actually \( \frac{71}{3} \), but not reflective of my interpretation).

None of the options correlate directly to \(\frac{4}{3}\), so please confirm any possible misinterpretation or I might advise selecting the option that represents the closest integer derived from my initial conclusion, not exact.

Based on the provided options and for a direct choice, I would go with \(-\frac{2}{3}\) since it's the only simple fractional representation that seems remotely related, despite not aligning with the solution derived.

Please double-check the calculation or options available for accuracy. Thank you!