What Is 1/6 ÷ 1/3?

Q: What is 1/6 ÷ 1/3?

1/6 ÷ 1/3 = 1/2 (0.5 as a decimal).

1/6 ÷ 1/3 = 1/2, which is 0.5 as a decimal.

Result

Answer

\frac{1}{6} \div \frac{1}{3} = \textcolor{#0b5c56}{\frac{1}{2}}

The quotient is 1/2 in simplest form.

Decimal: \displaystyle 0.5
Percent: 50%

1 of 2 equal parts

Step-by-step solution

The problem

\frac{1}{6} \div \frac{1}{3}

Flip \displaystyle \frac{1}{3} and multiply. 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}{6}} \times \textcolor{#0b5c56}{3}
Cancel common factors. Divide 3 and 6 by 3.
= \dfrac{1}{\cancel{6}_{\,\textcolor{#0b5c56}{2}}} \times \dfrac{\cancel{3}^{\,\textcolor{#0b5c56}{1}}}{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{1}{6} \div \frac{1}{3} \\[8pt]  &= \frac{1}{6} \times 3 && \textcolor{#5b6660}{\textsf{flip}} \\[8pt]  &= \dfrac{1}{\cancel{6}_{\,2}} \times \dfrac{\cancel{3}^{\,1}}{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}

The answer in other forms

Simplest form	1/2
Decimal	0.5
Percent	50%
Same fractions	1/3 + 1/6, 1/3 − 1/6, 1/3 × 1/6

1/6 divided by other fractions

Sum	Answer
1/6 ÷ 1/2	1/3
1/6 ÷ 1/3	1/2
1/6 ÷ 2/3	1/4
1/6 ÷ 1/4	2/3
1/6 ÷ 3/4	2/9
1/6 ÷ 1/5	5/6
1/6 ÷ 2/5	5/12
1/6 ÷ 3/5	5/18
1/6 ÷ 4/5	5/24
1/6 ÷ 5/6	1/5
1/6 ÷ 1/8	4/3
1/6 ÷ 3/8	4/9
1/6 ÷ 5/8	4/15
1/6 ÷ 7/8	4/21