Answer
\frac{2}{3} \div \frac{1}{4} = \textcolor{#0b5c56}{\frac{8}{3} = 2\frac{2}{3}}
The quotient is 8/3 in simplest form, or 2 2/3 as a mixed number.
Decimal: \displaystyle 2.\overline{6} Percent: 266.67% 2 wholes + 2 of 3 equal parts
Step-by-step solution The problem
\frac{2}{3} \div \frac{1}{4}
Flip \displaystyle \frac{1}{4} Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{1}{4} \;\rightarrow\; \frac{4}{1}
= \textcolor{#0b5c56}{\frac{2}{3}} \times \textcolor{#0b5c56}{4}
Multiply. A whole number is itself over 1. Top times top, bottom times bottom.
= \frac{2 \times 4}{3 \times 1} = \textcolor{#0b5c56}{\frac{8}{3}}
Check that it can't be simplified. 8 and 3 have no common factor other than 1, so this is the simplest form.
\text{GCF}(8, 3) = 1
Write it as a mixed number. Divide: 3 goes into 8 2 times with 2 left over. The whole number is 2, the remainder 2 becomes the numerator, and the denominator stays 3.
8 \div 3 = 2\ \text{R}\ 2
= \textcolor{#0b5c56}{2\frac{2}{3}}
All the working together \begin{aligned} &\frac{2}{3} \div \frac{1}{4} \\[8pt] &= \frac{2}{3} \times 4 && \textcolor{#5b6660}{\textsf{flip}} \\[8pt] &= \frac{2 \times 4}{3 \times 1} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt] &= \frac{8}{3} \\[8pt] &= \textcolor{#0b5c56}{2\frac{2}{3}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}