Question

question 6 of 8
what is the quotient of \\(\frac{ - \frac{1}{6} }{0.2}\\)?
\\(\circ\\) \\(\frac{5}{6}\\)
\\(\circ\\) \\(\frac{1}{30}\\)
\\(\circ\\) \\(-\frac{5}{6}\\)
\\(\circ\\) \\(-\frac{1}{30}\\)

Explanation:

Step1: Convert decimal to fraction

0.2 can be written as $\frac{1}{5}$. So the expression becomes $\frac{-\frac{1}{6}}{\frac{1}{5}}$.

Step2: Divide fractions (multiply by reciprocal)

Dividing by a fraction is multiplying by its reciprocal. So $\frac{-\frac{1}{6}}{\frac{1}{5}} = -\frac{1}{6} \times 5$.

Step3: Multiply the numbers

$-\frac{1}{6} \times 5 = -\frac{5}{6}$? Wait, no, wait: Wait, $\frac{-\frac{1}{6}}{\frac{1}{5}}$ is $-\frac{1}{6} \div \frac{1}{5} = -\frac{1}{6} \times 5 = -\frac{5}{6}$? Wait, no, wait, 0.2 is $\frac{1}{5}$, so the division is $(-\frac{1}{6}) \div \frac{1}{5} = (-\frac{1}{6}) \times 5 = -\frac{5}{6}$? Wait, but let's check again. Wait, the original problem is $\frac{-\frac{1}{6}}{0.2}$. So 0.2 is $\frac{1}{5}$, so it's $(-\frac{1}{6}) \div \frac{1}{5} = (-\frac{1}{6}) \times 5 = -\frac{5}{6}$? Wait, but let's compute: $-\frac{1}{6} \div 0.2 = -\frac{1}{6} \div \frac{1}{5} = -\frac{1}{6} \times 5 = -\frac{5}{6}$. Wait, but let's check the options. The third option is $-\frac{5}{6}$? Wait, no, the third option is $-\frac{5}{6}$? Wait, the options are:

1. $\frac{5}{6}$

1. $\frac{1}{30}$

1. $-\frac{5}{6}$

1. $-\frac{1}{30}$

Wait, so after calculation, we get $-\frac{5}{6}$? Wait, no, wait: Wait, 0.2 is $\frac{1}{5}$, so dividing $-\frac{1}{6}$ by $\frac{1}{5}$ is $-\frac{1}{6} \times 5 = -\frac{5}{6}$. Yes. So the correct answer is $-\frac{5}{6}$.

Wait, but let's recheck:

$\frac{-\frac{1}{6}}{0.2} = -\frac{1}{6} \div 0.2$

0.2 is $\frac{1}{5}$, so:

$-\frac{1}{6} \div \frac{1}{5} = -\frac{1}{6} \times 5 = -\frac{5}{6}$

Yes. So the answer is $-\frac{5}{6}$.

Answer:

$-\frac{5}{6}$ (corresponding to the option with $-\frac{5}{6}$)