Answer
\frac{3}{8} \div \frac{3}{4} = \textcolor{#0b5c56}{\frac{1}{2}}
The quotient is 1/2 in simplest form.
- Decimal:
\displaystyle 0.5 - Percent: 50%
Step-by-step solution
The problem
\frac{3}{8} \div \frac{3}{4}
Flip \displaystyle \frac{3}{4} and multiply. 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{3}{8}} \times \textcolor{#0b5c56}{\frac{4}{3}}
Cancel common factors. Divide 3 and 3 by 3; 4 and 8 by 4.
= \dfrac{\cancel{3}^{\,\textcolor{#0b5c56}{1}}}{\cancel{8}_{\,\textcolor{#0b5c56}{2}}} \times \dfrac{\cancel{4}^{\,\textcolor{#0b5c56}{1}}}{\cancel{3}_{\,\textcolor{#0b5c56}{1}}} = \textcolor{#0b5c56}{\frac{1}{2}} \times \textcolor{#0b5c56}{\frac{1}{1}}
Multiply. Top times top, bottom times bottom.
= \frac{1 \times 1}{2 \times 1} = \textcolor{#0b5c56}{\frac{1}{2}}
All the working together
\begin{aligned} &\frac{3}{8} \div \frac{3}{4} \\[8pt] &= \frac{3}{8} \times \frac{4}{3} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt] &= \dfrac{\cancel{3}^{\,1}}{\cancel{8}_{\,2}} \times \dfrac{\cancel{4}^{\,1}}{\cancel{3}_{\,1}} && \textcolor{#5b6660}{\textsf{cancel}} \\[8pt] &= \frac{1}{2} \times \frac{1}{1} \\[8pt] &= \frac{1 \times 1}{2 \times 1} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt] &= \textcolor{#0b5c56}{\frac{1}{2}}\end{aligned}