What Is 2/3 ÷ 3/4?

Q: What is 2/3 ÷ 3/4?

2/3 ÷ 3/4 = 8/9 (0.8889 as a decimal).

2/3 ÷ 3/4 = 8/9, about 0.889 as a decimal.

Result

Answer

\frac{2}{3} \div \frac{3}{4} = \textcolor{#0b5c56}{\frac{8}{9}}

The quotient is 8/9 in simplest form.

Decimal: \displaystyle 0.\overline{8} (the 8 repeats forever, about 0.8889)
Percent: 88.89%

8 of 9 equal parts

Step-by-step solution

The problem

\frac{2}{3} \div \frac{3}{4}

Flip \displaystyle \frac{3}{4} and multiply. Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{3}{4} \;\rightarrow\; \frac{4}{3}
= \textcolor{#0b5c56}{\frac{2}{3}} \times \textcolor{#0b5c56}{\frac{4}{3}}
Multiply. Top times top, bottom times bottom.
= \frac{2 \times 4}{3 \times 3} = \textcolor{#0b5c56}{\frac{8}{9}}
Check that it can't be simplified. 8 and 9 have no common factor other than 1, so this is the simplest form.
\text{GCF}(8, 9) = 1

All the working together

\begin{aligned} &\frac{2}{3} \div \frac{3}{4} \\[8pt]  &= \frac{2}{3} \times \frac{4}{3} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt]  &= \frac{2 \times 4}{3 \times 3} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{8}{9}}\end{aligned}

The answer in other forms

Simplest form	8/9
Decimal	0.888… (the 8 repeats forever)
Percent	≈ 88.89%
Same fractions	2/3 + 3/4, 3/4 − 2/3, 2/3 × 3/4

2/3 divided by other fractions

Sum	Answer
2/3 ÷ 1/2	4/3
2/3 ÷ 1/3	2
2/3 ÷ 1/4	8/3
2/3 ÷ 3/4	8/9
2/3 ÷ 1/5	10/3
2/3 ÷ 2/5	5/3
2/3 ÷ 3/5	10/9
2/3 ÷ 4/5	5/6
2/3 ÷ 1/6	4
2/3 ÷ 5/6	4/5
2/3 ÷ 1/8	16/3
2/3 ÷ 3/8	16/9
2/3 ÷ 5/8	16/15
2/3 ÷ 7/8	16/21