What Is 2/5 ÷ 3/5?

Q: What is 2/5 ÷ 3/5?

2/5 ÷ 3/5 = 2/3 (0.6667 as a decimal).

2/5 ÷ 3/5 = 2/3, about 0.667 as a decimal.

Result

Answer

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

The quotient is 2/3 in simplest form.

Decimal: \displaystyle 0.\overline{6} (the 6 repeats forever, about 0.6667)
Percent: 66.67%

2 of 3 equal parts

Step-by-step solution

The problem

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

Flip \displaystyle \frac{3}{5} and multiply. Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{3}{5} \;\rightarrow\; \frac{5}{3}
= \textcolor{#0b5c56}{\frac{2}{5}} \times \textcolor{#0b5c56}{\frac{5}{3}}
Cancel common factors. Divide 5 and 5 by 5.
= \dfrac{2}{\cancel{5}_{\,\textcolor{#0b5c56}{1}}} \times \dfrac{\cancel{5}^{\,\textcolor{#0b5c56}{1}}}{3} = \textcolor{#0b5c56}{\frac{2}{1}} \times \textcolor{#0b5c56}{\frac{1}{3}}
Multiply. Top times top, bottom times bottom.
= \frac{2 \times 1}{1 \times 3} = \textcolor{#0b5c56}{\frac{2}{3}}

All the working together

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

The answer in other forms

Simplest form	2/3
Decimal	0.666… (the 6 repeats forever)
Percent	≈ 66.67%
Same fractions	2/5 + 3/5, 3/5 − 2/5, 2/5 × 3/5

2/5 divided by other fractions

Sum	Answer
2/5 ÷ 1/2	4/5
2/5 ÷ 1/3	6/5
2/5 ÷ 2/3	3/5
2/5 ÷ 1/4	8/5
2/5 ÷ 3/4	8/15
2/5 ÷ 1/5	2
2/5 ÷ 3/5	2/3
2/5 ÷ 4/5	1/2
2/5 ÷ 1/6	12/5
2/5 ÷ 5/6	12/25
2/5 ÷ 1/8	16/5
2/5 ÷ 3/8	16/15
2/5 ÷ 5/8	16/25
2/5 ÷ 7/8	16/35