Answer
\frac{1}{3} \div \frac{2}{3} = \textcolor{#0b5c56}{\frac{1}{2}}
The quotient is 1/2 in simplest form.
- Decimal:
\displaystyle 0.5 - Percent: 50%
Step-by-step solution
The problem
\frac{1}{3} \div \frac{2}{3}
Flip \displaystyle \frac{2}{3} and multiply. 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{1}{3}} \times \textcolor{#0b5c56}{\frac{3}{2}}
Cancel common factors. Divide 3 and 3 by 3.
= \dfrac{1}{\cancel{3}_{\,\textcolor{#0b5c56}{1}}} \times \dfrac{\cancel{3}^{\,\textcolor{#0b5c56}{1}}}{2} = \textcolor{#0b5c56}{\frac{1}{1}} \times \textcolor{#0b5c56}{\frac{1}{2}}
Multiply. Top times top, bottom times bottom.
= \frac{1 \times 1}{1 \times 2} = \textcolor{#0b5c56}{\frac{1}{2}}
All the working together
\begin{aligned} &\frac{1}{3} \div \frac{2}{3} \\[8pt] &= \frac{1}{3} \times \frac{3}{2} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt] &= \dfrac{1}{\cancel{3}_{\,1}} \times \dfrac{\cancel{3}^{\,1}}{2} && \textcolor{#5b6660}{\textsf{cancel}} \\[8pt] &= \frac{1}{1} \times \frac{1}{2} \\[8pt] &= \frac{1 \times 1}{1 \times 2} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt] &= \textcolor{#0b5c56}{\frac{1}{2}}\end{aligned}