What Is 1/2 ÷ 3/5?

Q: What is 1/2 ÷ 3/5?

1/2 ÷ 3/5 = 5/6 (0.8333 as a decimal).

1/2 ÷ 3/5 = 5/6, about 0.833 as a decimal.

Result

Answer

\frac{1}{2} \div \frac{3}{5} = \textcolor{#0b5c56}{\frac{5}{6}}

The quotient is 5/6 in simplest form.

Decimal: \displaystyle 0.8\overline{3} (the 3 repeats forever, about 0.8333)
Percent: 83.33%

5 of 6 equal parts

Step-by-step solution

The problem

\frac{1}{2} \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}{2}} \times \textcolor{#0b5c56}{\frac{5}{3}}
Multiply. Top times top, bottom times bottom.
= \frac{1 \times 5}{2 \times 3} = \textcolor{#0b5c56}{\frac{5}{6}}
Check that it can't be simplified. 5 and 6 have no common factor other than 1, so this is the simplest form.
\text{GCF}(5, 6) = 1

All the working together

\begin{aligned} &\frac{1}{2} \div \frac{3}{5} \\[8pt]  &= \frac{1}{2} \times \frac{5}{3} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt]  &= \frac{1 \times 5}{2 \times 3} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{5}{6}}\end{aligned}

The answer in other forms

Simplest form	5/6
Decimal	0.8333… (the 3 repeats forever)
Percent	≈ 83.33%
Same fractions	1/2 + 3/5, 3/5 − 1/2, 1/2 × 3/5

1/2 divided by other fractions

Sum	Answer
1/2 ÷ 1/3	3/2
1/2 ÷ 2/3	3/4
1/2 ÷ 1/4	2
1/2 ÷ 3/4	2/3
1/2 ÷ 1/5	5/2
1/2 ÷ 2/5	5/4
1/2 ÷ 3/5	5/6
1/2 ÷ 4/5	5/8
1/2 ÷ 1/6	3
1/2 ÷ 5/6	3/5
1/2 ÷ 1/8	4
1/2 ÷ 3/8	4/3
1/2 ÷ 5/8	4/5
1/2 ÷ 7/8	4/7