What Is 4/5 × 5/6?

Q: What is 4/5 × 5/6?

4/5 × 5/6 = 2/3 (0.6667 as a decimal).

4/5 × 5/6 = 2/3, about 0.667 as a decimal.

Result

Answer

\frac{4}{5} \times \frac{5}{6} = \textcolor{#0b5c56}{\frac{2}{3}}

The product 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{4}{5} \times \frac{5}{6}

Cancel common factors. Divide 4 and 6 by 2; 5 and 5 by 5.
= \dfrac{\cancel{4}^{\,\textcolor{#0b5c56}{2}}}{\cancel{5}_{\,\textcolor{#0b5c56}{1}}} \times \dfrac{\cancel{5}^{\,\textcolor{#0b5c56}{1}}}{\cancel{6}_{\,\textcolor{#0b5c56}{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{4}{5} \times \frac{5}{6} \\[8pt]  &= \dfrac{\cancel{4}^{\,2}}{\cancel{5}_{\,1}} \times \dfrac{\cancel{5}^{\,1}}{\cancel{6}_{\,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	4/5 + 5/6, 5/6 − 4/5, 4/5 ÷ 5/6

4/5 times other fractions

Sum	Answer
4/5 × 1/2	2/5
4/5 × 1/3	4/15
4/5 × 2/3	8/15
4/5 × 1/4	1/5
4/5 × 3/4	3/5
4/5 × 1/5	4/25
4/5 × 2/5	8/25
4/5 × 3/5	12/25
4/5 × 4/5	16/25
4/5 × 1/6	2/15
4/5 × 5/6	2/3
4/5 × 1/8	1/10
4/5 × 3/8	3/10
4/5 × 5/8	1/2
4/5 × 7/8	7/10