Answer
\frac{1}{2} \div \frac{7}{8} = \textcolor{#0b5c56}{\frac{4}{7}}
The quotient is 4/7 in simplest form.
- Decimal:
\displaystyle 0.\overline{571428} (the 571428 repeats forever, about 0.5714) - Percent: 57.14%
Step-by-step solution
The problem
\frac{1}{2} \div \frac{7}{8}
Flip \displaystyle \frac{7}{8} and multiply. Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{7}{8} \;\rightarrow\; \frac{8}{7}
= \textcolor{#0b5c56}{\frac{1}{2}} \times \textcolor{#0b5c56}{\frac{8}{7}}
Cancel common factors. Divide 8 and 2 by 2.
= \dfrac{1}{\cancel{2}_{\,\textcolor{#0b5c56}{1}}} \times \dfrac{\cancel{8}^{\,\textcolor{#0b5c56}{4}}}{7} = \textcolor{#0b5c56}{\frac{1}{1}} \times \textcolor{#0b5c56}{\frac{4}{7}}
Multiply. Top times top, bottom times bottom.
= \frac{1 \times 4}{1 \times 7} = \textcolor{#0b5c56}{\frac{4}{7}}
All the working together
\begin{aligned} &\frac{1}{2} \div \frac{7}{8} \\[8pt] &= \frac{1}{2} \times \frac{8}{7} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt] &= \dfrac{1}{\cancel{2}_{\,1}} \times \dfrac{\cancel{8}^{\,4}}{7} && \textcolor{#5b6660}{\textsf{cancel}} \\[8pt] &= \frac{1}{1} \times \frac{4}{7} \\[8pt] &= \frac{1 \times 4}{1 \times 7} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt] &= \textcolor{#0b5c56}{\frac{4}{7}}\end{aligned}