Answer
\frac{5}{6} \div \frac{1}{2} = \textcolor{#0b5c56}{\frac{5}{3} = 1\frac{2}{3}}
The quotient is 5/3 in simplest form, or 1 2/3 as a mixed number.
Decimal: \displaystyle 1.\overline{6} Percent: 166.67% 1 whole + 2 of 3 equal parts
Step-by-step solution The problem
\frac{5}{6} \div \frac{1}{2}
Flip \displaystyle \frac{1}{2} Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{1}{2} \;\rightarrow\; \frac{2}{1}
= \textcolor{#0b5c56}{\frac{5}{6}} \times \textcolor{#0b5c56}{2}
Cancel common factors. Divide 2 and 6 by 2.
= \dfrac{5}{\cancel{6}_{\,\textcolor{#0b5c56}{3}}} \times \dfrac{\cancel{2}^{\,\textcolor{#0b5c56}{1}}}{1} = \textcolor{#0b5c56}{\frac{5}{3}} \times \textcolor{#0b5c56}{\frac{1}{1}}
Multiply. Top times top, bottom times bottom.
= \frac{5 \times 1}{3 \times 1} = \textcolor{#0b5c56}{\frac{5}{3}}
Write it as a mixed number. Divide: 3 goes into 5 1 time with 2 left over. The whole number is 1, the remainder 2 becomes the numerator, and the denominator stays 3.
5 \div 3 = 1\ \text{R}\ 2
= \textcolor{#0b5c56}{1\frac{2}{3}}
All the working together \begin{aligned} &\frac{5}{6} \div \frac{1}{2} \\[8pt] &= \frac{5}{6} \times 2 && \textcolor{#5b6660}{\textsf{flip}} \\[8pt] &= \dfrac{5}{\cancel{6}_{\,3}} \times \dfrac{\cancel{2}^{\,1}}{1} && \textcolor{#5b6660}{\textsf{cancel}} \\[8pt] &= \frac{5}{3} \times \frac{1}{1} \\[8pt] &= \frac{5 \times 1}{3 \times 1} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt] &= \frac{5}{3} \\[8pt] &= \textcolor{#0b5c56}{1\frac{2}{3}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}