Answer
\frac{5}{6} \div \frac{1}{8} = \textcolor{#0b5c56}{\frac{20}{3} = 6\frac{2}{3}}
The quotient is 20/3 in simplest form, or 6 2/3 as a mixed number.
- Decimal:
\displaystyle 6.\overline{6} (the 6 repeats forever, about 6.6667) - Percent: 666.67%
Step-by-step solution
The problem
\frac{5}{6} \div \frac{1}{8}
Flip \displaystyle \frac{1}{8} and multiply. Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{1}{8} \;\rightarrow\; \frac{8}{1}
= \textcolor{#0b5c56}{\frac{5}{6}} \times \textcolor{#0b5c56}{8}
Cancel common factors. Divide 8 and 6 by 2.
= \dfrac{5}{\cancel{6}_{\,\textcolor{#0b5c56}{3}}} \times \dfrac{\cancel{8}^{\,\textcolor{#0b5c56}{4}}}{1} = \textcolor{#0b5c56}{\frac{5}{3}} \times \textcolor{#0b5c56}{\frac{4}{1}}
Multiply. Top times top, bottom times bottom.
= \frac{5 \times 4}{3 \times 1} = \textcolor{#0b5c56}{\frac{20}{3}}
Write it as a mixed number. Divide: 3 goes into 20 6 times with 2 left over. The whole number is 6, the remainder 2 becomes the numerator, and the denominator stays 3.
20 \div 3 = 6\ \text{R}\ 2
= \textcolor{#0b5c56}{6\frac{2}{3}}
All the working together
\begin{aligned} &\frac{5}{6} \div \frac{1}{8} \\[8pt] &= \frac{5}{6} \times 8 && \textcolor{#5b6660}{\textsf{flip}} \\[8pt] &= \dfrac{5}{\cancel{6}_{\,3}} \times \dfrac{\cancel{8}^{\,4}}{1} && \textcolor{#5b6660}{\textsf{cancel}} \\[8pt] &= \frac{5}{3} \times \frac{4}{1} \\[8pt] &= \frac{5 \times 4}{3 \times 1} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt] &= \frac{20}{3} \\[8pt] &= \textcolor{#0b5c56}{6\frac{2}{3}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}