Answer
\frac{3}{4} \div \frac{1}{2} = \textcolor{#0b5c56}{\frac{3}{2} = 1\frac{1}{2}}
The quotient is 3/2 in simplest form, or 1 1/2 as a mixed number.
Decimal: \displaystyle 1.5 Percent: 150% 1 whole + 1 of 2 equal parts
Step-by-step solution The problem
\frac{3}{4} \div \frac{1}{2}
Flip \displaystyle \frac{1}{2} Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{1}{2} \;\rightarrow\; \frac{2}{1}
= \textcolor{#0b5c56}{\frac{3}{4}} \times \textcolor{#0b5c56}{2}
Cancel common factors. Divide 2 and 4 by 2.
= \dfrac{3}{\cancel{4}_{\,\textcolor{#0b5c56}{2}}} \times \dfrac{\cancel{2}^{\,\textcolor{#0b5c56}{1}}}{1} = \textcolor{#0b5c56}{\frac{3}{2}} \times \textcolor{#0b5c56}{\frac{1}{1}}
Multiply. Top times top, bottom times bottom.
= \frac{3 \times 1}{2 \times 1} = \textcolor{#0b5c56}{\frac{3}{2}}
Write it as a mixed number. Divide: 2 goes into 3 1 time with 1 left over. The whole number is 1, the remainder 1 becomes the numerator, and the denominator stays 2.
3 \div 2 = 1\ \text{R}\ 1
= \textcolor{#0b5c56}{1\frac{1}{2}}
All the working together \begin{aligned} &\frac{3}{4} \div \frac{1}{2} \\[8pt] &= \frac{3}{4} \times 2 && \textcolor{#5b6660}{\textsf{flip}} \\[8pt] &= \dfrac{3}{\cancel{4}_{\,2}} \times \dfrac{\cancel{2}^{\,1}}{1} && \textcolor{#5b6660}{\textsf{cancel}} \\[8pt] &= \frac{3}{2} \times \frac{1}{1} \\[8pt] &= \frac{3 \times 1}{2 \times 1} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt] &= \frac{3}{2} \\[8pt] &= \textcolor{#0b5c56}{1\frac{1}{2}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}