What Is 1/2 × 2/3?

Q: What is 1/2 × 2/3?

1/2 × 2/3 = 1/3 (0.3333 as a decimal).

1/2 × 2/3 = 1/3, about 0.333 as a decimal.

Result

Answer

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

The product is 1/3 in simplest form.

Decimal: \displaystyle 0.\overline{3} (the 3 repeats forever, about 0.3333)
Percent: 33.33%

1 of 3 equal parts

Step-by-step solution

The problem

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

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

All the working together

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

The answer in other forms

Simplest form	1/3
Decimal	0.333… (the 3 repeats forever)
Percent	≈ 33.33%
Same fractions	1/2 + 2/3, 2/3 − 1/2, 1/2 ÷ 2/3

1/2 times other fractions

Sum	Answer
1/2 × 1/2	1/4
1/2 × 1/3	1/6
1/2 × 2/3	1/3
1/2 × 1/4	1/8
1/2 × 3/4	3/8
1/2 × 1/5	1/10
1/2 × 2/5	1/5
1/2 × 3/5	3/10
1/2 × 4/5	2/5
1/2 × 1/6	1/12
1/2 × 5/6	5/12
1/2 × 1/8	1/16
1/2 × 3/8	3/16
1/2 × 5/8	5/16
1/2 × 7/8	7/16