What Is 1/5 ÷ 2/3?

Q: What is 1/5 ÷ 2/3?

1/5 ÷ 2/3 = 3/10 (0.3 as a decimal).

1/5 ÷ 2/3 = 3/10, which is 0.3 as a decimal.

Result

Answer

\frac{1}{5} \div \frac{2}{3} = \textcolor{#0b5c56}{\frac{3}{10}}

The quotient is 3/10 in simplest form.

Decimal: \displaystyle 0.3
Percent: 30%

3 of 10 equal parts

Step-by-step solution

The problem

\frac{1}{5} \div \frac{2}{3}

Flip \displaystyle \frac{2}{3} and multiply. Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{2}{3} \;\rightarrow\; \frac{3}{2}
= \textcolor{#0b5c56}{\frac{1}{5}} \times \textcolor{#0b5c56}{\frac{3}{2}}
Multiply. Top times top, bottom times bottom.
= \frac{1 \times 3}{5 \times 2} = \textcolor{#0b5c56}{\frac{3}{10}}
Check that it can't be simplified. 3 and 10 have no common factor other than 1, so this is the simplest form.
\text{GCF}(3, 10) = 1

All the working together

\begin{aligned} &\frac{1}{5} \div \frac{2}{3} \\[8pt]  &= \frac{1}{5} \times \frac{3}{2} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt]  &= \frac{1 \times 3}{5 \times 2} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{3}{10}}\end{aligned}

The answer in other forms

Simplest form	3/10
Decimal	0.3
Percent	30%
Same fractions	2/3 + 1/5, 2/3 − 1/5, 2/3 × 1/5

1/5 divided by other fractions

Sum	Answer
1/5 ÷ 1/2	2/5
1/5 ÷ 1/3	3/5
1/5 ÷ 2/3	3/10
1/5 ÷ 1/4	4/5
1/5 ÷ 3/4	4/15
1/5 ÷ 2/5	1/2
1/5 ÷ 3/5	1/3
1/5 ÷ 4/5	1/4
1/5 ÷ 1/6	6/5
1/5 ÷ 5/6	6/25
1/5 ÷ 1/8	8/5
1/5 ÷ 3/8	8/15
1/5 ÷ 5/8	8/25
1/5 ÷ 7/8	8/35