Answer
\frac{5}{6} \div \frac{2}{3} = \textcolor{#0b5c56}{\frac{5}{4} = 1\frac{1}{4}}
The quotient is 5/4 in simplest form, or 1 1/4 as a mixed number.
Decimal: \displaystyle 1.25 Percent: 125% 1 whole + 1 of 4 equal parts
Step-by-step solution The problem
\frac{5}{6} \div \frac{2}{3}
Flip \displaystyle \frac{2}{3} Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{2}{3} \;\rightarrow\; \frac{3}{2}
= \textcolor{#0b5c56}{\frac{5}{6}} \times \textcolor{#0b5c56}{\frac{3}{2}}
Cancel common factors. Divide 3 and 6 by 3.
= \dfrac{5}{\cancel{6}_{\,\textcolor{#0b5c56}{2}}} \times \dfrac{\cancel{3}^{\,\textcolor{#0b5c56}{1}}}{2} = \textcolor{#0b5c56}{\frac{5}{2}} \times \textcolor{#0b5c56}{\frac{1}{2}}
Multiply. Top times top, bottom times bottom.
= \frac{5 \times 1}{2 \times 2} = \textcolor{#0b5c56}{\frac{5}{4}}
Write it as a mixed number. Divide: 4 goes into 5 1 time with 1 left over. The whole number is 1, the remainder 1 becomes the numerator, and the denominator stays 4.
5 \div 4 = 1\ \text{R}\ 1
= \textcolor{#0b5c56}{1\frac{1}{4}}
All the working together \begin{aligned} &\frac{5}{6} \div \frac{2}{3} \\[8pt] &= \frac{5}{6} \times \frac{3}{2} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt] &= \dfrac{5}{\cancel{6}_{\,2}} \times \dfrac{\cancel{3}^{\,1}}{2} && \textcolor{#5b6660}{\textsf{cancel}} \\[8pt] &= \frac{5}{2} \times \frac{1}{2} \\[8pt] &= \frac{5 \times 1}{2 \times 2} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt] &= \frac{5}{4} \\[8pt] &= \textcolor{#0b5c56}{1\frac{1}{4}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}