Answer
\frac{5}{6} \div \frac{4}{5} = \textcolor{#0b5c56}{\frac{25}{24} = 1\frac{1}{24}}
The quotient is 25/24 in simplest form, or 1 1/24 as a mixed number.
Decimal: \displaystyle 1.041\overline{6} Percent: 104.17% 1 whole + 1 of 24 equal parts
Step-by-step solution The problem
\frac{5}{6} \div \frac{4}{5}
Flip \displaystyle \frac{4}{5} Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{4}{5} \;\rightarrow\; \frac{5}{4}
= \textcolor{#0b5c56}{\frac{5}{6}} \times \textcolor{#0b5c56}{\frac{5}{4}}
Multiply. Top times top, bottom times bottom.
= \frac{5 \times 5}{6 \times 4} = \textcolor{#0b5c56}{\frac{25}{24}}
Check that it can't be simplified. 25 and 24 have no common factor other than 1, so this is the simplest form.
\text{GCF}(25, 24) = 1
Write it as a mixed number. Divide: 24 goes into 25 1 time with 1 left over. The whole number is 1, the remainder 1 becomes the numerator, and the denominator stays 24.
25 \div 24 = 1\ \text{R}\ 1
= \textcolor{#0b5c56}{1\frac{1}{24}}
All the working together \begin{aligned} &\frac{5}{6} \div \frac{4}{5} \\[8pt] &= \frac{5}{6} \times \frac{5}{4} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt] &= \frac{5 \times 5}{6 \times 4} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt] &= \frac{25}{24} \\[8pt] &= \textcolor{#0b5c56}{1\frac{1}{24}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}