Answer
\frac{1}{6} \div \frac{1}{8} = \textcolor{#0b5c56}{\frac{4}{3} = 1\frac{1}{3}}
The quotient is 4/3 in simplest form, or 1 1/3 as a mixed number.
Decimal: \displaystyle 1.\overline{3} Percent: 133.33% 1 whole + 1 of 3 equal parts
Step-by-step solution The problem
\frac{1}{6} \div \frac{1}{8}
Flip \displaystyle \frac{1}{8} 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{1}{6}} \times \textcolor{#0b5c56}{8}
Cancel common factors. Divide 8 and 6 by 2.
= \dfrac{1}{\cancel{6}_{\,\textcolor{#0b5c56}{3}}} \times \dfrac{\cancel{8}^{\,\textcolor{#0b5c56}{4}}}{1} = \textcolor{#0b5c56}{\frac{1}{3}} \times \textcolor{#0b5c56}{\frac{4}{1}}
Multiply. Top times top, bottom times bottom.
= \frac{1 \times 4}{3 \times 1} = \textcolor{#0b5c56}{\frac{4}{3}}
Write it as a mixed number. Divide: 3 goes into 4 1 time with 1 left over. The whole number is 1, the remainder 1 becomes the numerator, and the denominator stays 3.
4 \div 3 = 1\ \text{R}\ 1
= \textcolor{#0b5c56}{1\frac{1}{3}}
All the working together \begin{aligned} &\frac{1}{6} \div \frac{1}{8} \\[8pt] &= \frac{1}{6} \times 8 && \textcolor{#5b6660}{\textsf{flip}} \\[8pt] &= \dfrac{1}{\cancel{6}_{\,3}} \times \dfrac{\cancel{8}^{\,4}}{1} && \textcolor{#5b6660}{\textsf{cancel}} \\[8pt] &= \frac{1}{3} \times \frac{4}{1} \\[8pt] &= \frac{1 \times 4}{3 \times 1} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt] &= \frac{4}{3} \\[8pt] &= \textcolor{#0b5c56}{1\frac{1}{3}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}