What Is 1/5 ÷ 3/5?

Q: What is 1/5 ÷ 3/5?

1/5 ÷ 3/5 = 1/3 (0.3333 as a decimal).

1/5 ÷ 3/5 = 1/3, about 0.333 as a decimal.

Result

Answer

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

The quotient 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}{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{1}{5}} \times \textcolor{#0b5c56}{\frac{5}{3}}
Cancel common factors. Divide 5 and 5 by 5.
= \dfrac{1}{\cancel{5}_{\,\textcolor{#0b5c56}{1}}} \times \dfrac{\cancel{5}^{\,\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}{5} \div \frac{3}{5} \\[8pt]  &= \frac{1}{5} \times \frac{5}{3} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt]  &= \dfrac{1}{\cancel{5}_{\,1}} \times \dfrac{\cancel{5}^{\,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	1/5 + 3/5, 3/5 − 1/5, 1/5 × 3/5

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