Answer
\frac{4}{5} \div \frac{2}{3} = \textcolor{#0b5c56}{\frac{6}{5} = 1\frac{1}{5}}
The quotient is 6/5 in simplest form, or 1 1/5 as a mixed number.
Decimal: \displaystyle 1.2 Percent: 120% 1 whole + 1 of 5 equal parts
Step-by-step solution The problem
\frac{4}{5} \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{4}{5}} \times \textcolor{#0b5c56}{\frac{3}{2}}
Cancel common factors. Divide 4 and 2 by 2.
= \dfrac{\cancel{4}^{\,\textcolor{#0b5c56}{2}}}{5} \times \dfrac{3}{\cancel{2}_{\,\textcolor{#0b5c56}{1}}} = \textcolor{#0b5c56}{\frac{2}{5}} \times \textcolor{#0b5c56}{\frac{3}{1}}
Multiply. Top times top, bottom times bottom.
= \frac{2 \times 3}{5 \times 1} = \textcolor{#0b5c56}{\frac{6}{5}}
Write it as a mixed number. Divide: 5 goes into 6 1 time with 1 left over. The whole number is 1, the remainder 1 becomes the numerator, and the denominator stays 5.
6 \div 5 = 1\ \text{R}\ 1
= \textcolor{#0b5c56}{1\frac{1}{5}}
All the working together \begin{aligned} &\frac{4}{5} \div \frac{2}{3} \\[8pt] &= \frac{4}{5} \times \frac{3}{2} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt] &= \dfrac{\cancel{4}^{\,2}}{5} \times \dfrac{3}{\cancel{2}_{\,1}} && \textcolor{#5b6660}{\textsf{cancel}} \\[8pt] &= \frac{2}{5} \times \frac{3}{1} \\[8pt] &= \frac{2 \times 3}{5 \times 1} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt] &= \frac{6}{5} \\[8pt] &= \textcolor{#0b5c56}{1\frac{1}{5}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}