What Is 4/5 ÷ 7/8?

Q: What is 4/5 ÷ 7/8?

4/5 ÷ 7/8 = 32/35 (0.9143 as a decimal).

4/5 ÷ 7/8 = 32/35, about 0.914 as a decimal.

Result

Answer

\frac{4}{5} \div \frac{7}{8} = \textcolor{#0b5c56}{\frac{32}{35}}

The quotient is 32/35 in simplest form.

Decimal: \displaystyle 0.9\overline{142857} (the 142857 repeats forever, about 0.9143)
Percent: 91.43%

32 of 35 equal parts

Step-by-step solution

The problem

\frac{4}{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{4}{5}} \times \textcolor{#0b5c56}{\frac{8}{7}}
Multiply. Top times top, bottom times bottom.
= \frac{4 \times 8}{5 \times 7} = \textcolor{#0b5c56}{\frac{32}{35}}
Check that it can't be simplified. 32 and 35 have no common factor other than 1, so this is the simplest form.
\text{GCF}(32, 35) = 1

All the working together

\begin{aligned} &\frac{4}{5} \div \frac{7}{8} \\[8pt]  &= \frac{4}{5} \times \frac{8}{7} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt]  &= \frac{4 \times 8}{5 \times 7} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{32}{35}}\end{aligned}

The answer in other forms

Simplest form	32/35
Decimal	0.9142857… (the 142857 repeats forever)
Percent	≈ 91.43%
Same fractions	4/5 + 7/8, 7/8 − 4/5, 4/5 × 7/8

4/5 divided by other fractions

Sum	Answer
4/5 ÷ 1/2	8/5
4/5 ÷ 1/3	12/5
4/5 ÷ 2/3	6/5
4/5 ÷ 1/4	16/5
4/5 ÷ 3/4	16/15
4/5 ÷ 1/5	4
4/5 ÷ 2/5	2
4/5 ÷ 3/5	4/3
4/5 ÷ 1/6	24/5
4/5 ÷ 5/6	24/25
4/5 ÷ 1/8	32/5
4/5 ÷ 3/8	32/15
4/5 ÷ 5/8	32/25
4/5 ÷ 7/8	32/35