Answer
\frac{5}{8} \div \frac{1}{6} = \textcolor{#0b5c56}{\frac{15}{4} = 3\frac{3}{4}}
The quotient is 15/4 in simplest form, or 3 3/4 as a mixed number.
Decimal: \displaystyle 3.75 Percent: 375% 3 wholes + 3 of 4 equal parts
Step-by-step solution The problem
\frac{5}{8} \div \frac{1}{6}
Flip \displaystyle \frac{1}{6} Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{1}{6} \;\rightarrow\; \frac{6}{1}
= \textcolor{#0b5c56}{\frac{5}{8}} \times \textcolor{#0b5c56}{6}
Cancel common factors. Divide 6 and 8 by 2.
= \dfrac{5}{\cancel{8}_{\,\textcolor{#0b5c56}{4}}} \times \dfrac{\cancel{6}^{\,\textcolor{#0b5c56}{3}}}{1} = \textcolor{#0b5c56}{\frac{5}{4}} \times \textcolor{#0b5c56}{\frac{3}{1}}
Multiply. Top times top, bottom times bottom.
= \frac{5 \times 3}{4 \times 1} = \textcolor{#0b5c56}{\frac{15}{4}}
Write it as a mixed number. Divide: 4 goes into 15 3 times with 3 left over. The whole number is 3, the remainder 3 becomes the numerator, and the denominator stays 4.
15 \div 4 = 3\ \text{R}\ 3
= \textcolor{#0b5c56}{3\frac{3}{4}}
All the working together \begin{aligned} &\frac{5}{8} \div \frac{1}{6} \\[8pt] &= \frac{5}{8} \times 6 && \textcolor{#5b6660}{\textsf{flip}} \\[8pt] &= \dfrac{5}{\cancel{8}_{\,4}} \times \dfrac{\cancel{6}^{\,3}}{1} && \textcolor{#5b6660}{\textsf{cancel}} \\[8pt] &= \frac{5}{4} \times \frac{3}{1} \\[8pt] &= \frac{5 \times 3}{4 \times 1} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt] &= \frac{15}{4} \\[8pt] &= \textcolor{#0b5c56}{3\frac{3}{4}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}