Answer
\frac{4}{5} \div \frac{3}{4} = \textcolor{#0b5c56}{\frac{16}{15} = 1\frac{1}{15}}
The quotient is 16/15 in simplest form, or 1 1/15 as a mixed number.
Decimal: \displaystyle 1.0\overline{6} Percent: 106.67% 1 whole + 1 of 15 equal parts
Step-by-step solution The problem
\frac{4}{5} \div \frac{3}{4}
Flip \displaystyle \frac{3}{4} Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{3}{4} \;\rightarrow\; \frac{4}{3}
= \textcolor{#0b5c56}{\frac{4}{5}} \times \textcolor{#0b5c56}{\frac{4}{3}}
Multiply. Top times top, bottom times bottom.
= \frac{4 \times 4}{5 \times 3} = \textcolor{#0b5c56}{\frac{16}{15}}
Check that it can't be simplified. 16 and 15 have no common factor other than 1, so this is the simplest form.
\text{GCF}(16, 15) = 1
Write it as a mixed number. Divide: 15 goes into 16 1 time with 1 left over. The whole number is 1, the remainder 1 becomes the numerator, and the denominator stays 15.
16 \div 15 = 1\ \text{R}\ 1
= \textcolor{#0b5c56}{1\frac{1}{15}}
All the working together \begin{aligned} &\frac{4}{5} \div \frac{3}{4} \\[8pt] &= \frac{4}{5} \times \frac{4}{3} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt] &= \frac{4 \times 4}{5 \times 3} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt] &= \frac{16}{15} \\[8pt] &= \textcolor{#0b5c56}{1\frac{1}{15}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}