What Is 2/3 × 1/6?

Q: What is 2/3 × 1/6?

2/3 × 1/6 = 1/9 (0.1111 as a decimal).

2/3 × 1/6 = 1/9, about 0.111 as a decimal.

Result

Answer

\frac{2}{3} \times \frac{1}{6} = \textcolor{#0b5c56}{\frac{1}{9}}

The product is 1/9 in simplest form.

Decimal: \displaystyle 0.\overline{1} (the 1 repeats forever, about 0.1111)
Percent: 11.11%

1 of 9 equal parts

Step-by-step solution

The problem

\frac{2}{3} \times \frac{1}{6}

Cancel common factors. Divide 2 and 6 by 2.
= \dfrac{\cancel{2}^{\,\textcolor{#0b5c56}{1}}}{3} \times \dfrac{1}{\cancel{6}_{\,\textcolor{#0b5c56}{3}}} = \textcolor{#0b5c56}{\frac{1}{3}} \times \textcolor{#0b5c56}{\frac{1}{3}}
Multiply. Top times top, bottom times bottom.
= \frac{1 \times 1}{3 \times 3} = \textcolor{#0b5c56}{\frac{1}{9}}

All the working together

\begin{aligned} &\frac{2}{3} \times \frac{1}{6} \\[8pt]  &= \dfrac{\cancel{2}^{\,1}}{3} \times \dfrac{1}{\cancel{6}_{\,3}} && \textcolor{#5b6660}{\textsf{cancel}} \\[8pt]  &= \frac{1}{3} \times \frac{1}{3} \\[8pt]  &= \frac{1 \times 1}{3 \times 3} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{1}{9}}\end{aligned}

The answer in other forms

Simplest form	1/9
Decimal	0.111… (the 1 repeats forever)
Percent	≈ 11.11%
Same fractions	2/3 + 1/6, 2/3 − 1/6, 2/3 ÷ 1/6

2/3 times other fractions

Sum	Answer
2/3 × 1/2	1/3
2/3 × 1/3	2/9
2/3 × 2/3	4/9
2/3 × 1/4	1/6
2/3 × 3/4	1/2
2/3 × 1/5	2/15
2/3 × 2/5	4/15
2/3 × 3/5	2/5
2/3 × 4/5	8/15
2/3 × 1/6	1/9
2/3 × 5/6	5/9
2/3 × 1/8	1/12
2/3 × 3/8	1/4
2/3 × 5/8	5/12
2/3 × 7/8	7/12