What Is 1/3 × 1/3?

Q: What is 1/3 × 1/3?

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

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

Result

Answer

\frac{1}{3} \times \frac{1}{3} = \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{1}{3} \times \frac{1}{3}

Multiply. Top times top, bottom times bottom.
= \frac{1 \times 1}{3 \times 3} = \textcolor{#0b5c56}{\frac{1}{9}}
Check that it can't be simplified. 1 and 9 have no common factor other than 1, so this is the simplest form.
\text{GCF}(1, 9) = 1

All the working together

\begin{aligned} &\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	1/3 + 1/3

1/3 times other fractions

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