Answer
\frac{1}{2} \div \frac{1}{3} = \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{1}{2} \div \frac{1}{3}
Flip \displaystyle \frac{1}{3} Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{1}{3} \;\rightarrow\; \frac{3}{1}
= \textcolor{#0b5c56}{\frac{1}{2}} \times \textcolor{#0b5c56}{3}
Multiply. A whole number is itself over 1. Top times top, bottom times bottom.
= \frac{1 \times 3}{2 \times 1} = \textcolor{#0b5c56}{\frac{3}{2}}
Check that it can't be simplified. 3 and 2 have no common factor other than 1, so this is the simplest form.
\text{GCF}(3, 2) = 1
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{1}{2} \div \frac{1}{3} \\[8pt] &= \frac{1}{2} \times 3 && \textcolor{#5b6660}{\textsf{flip}} \\[8pt] &= \frac{1 \times 3}{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}