What Is 2/5 ÷ 7/8?

Q: What is 2/5 ÷ 7/8?

2/5 ÷ 7/8 = 16/35 (0.4571 as a decimal).

2/5 ÷ 7/8 = 16/35, about 0.457 as a decimal.

Result

Answer

\frac{2}{5} \div \frac{7}{8} = \textcolor{#0b5c56}{\frac{16}{35}}

The quotient is 16/35 in simplest form.

Decimal: \displaystyle 0.4\overline{571428} (the 571428 repeats forever, about 0.4571)
Percent: 45.71%

16 of 35 equal parts

Step-by-step solution

The problem

\frac{2}{5} \div \frac{7}{8}

Flip \displaystyle \frac{7}{8} and multiply. Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{7}{8} \;\rightarrow\; \frac{8}{7}
= \textcolor{#0b5c56}{\frac{2}{5}} \times \textcolor{#0b5c56}{\frac{8}{7}}
Multiply. Top times top, bottom times bottom.
= \frac{2 \times 8}{5 \times 7} = \textcolor{#0b5c56}{\frac{16}{35}}
Check that it can't be simplified. 16 and 35 have no common factor other than 1, so this is the simplest form.
\text{GCF}(16, 35) = 1

All the working together

\begin{aligned} &\frac{2}{5} \div \frac{7}{8} \\[8pt]  &= \frac{2}{5} \times \frac{8}{7} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt]  &= \frac{2 \times 8}{5 \times 7} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{16}{35}}\end{aligned}

The answer in other forms

Simplest form	16/35
Decimal	0.4571428… (the 571428 repeats forever)
Percent	≈ 45.71%
Same fractions	2/5 + 7/8, 7/8 − 2/5, 2/5 × 7/8

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