What Is 3/5 ÷ 7/8?

Q: What is 3/5 ÷ 7/8?

3/5 ÷ 7/8 = 24/35 (0.6857 as a decimal).

3/5 ÷ 7/8 = 24/35, about 0.686 as a decimal.

Result

Answer

\frac{3}{5} \div \frac{7}{8} = \textcolor{#0b5c56}{\frac{24}{35}}

The quotient is 24/35 in simplest form.

Decimal: \displaystyle 0.6\overline{857142} (the 857142 repeats forever, about 0.6857)
Percent: 68.57%

24 of 35 equal parts

Step-by-step solution

The problem

\frac{3}{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{3}{5}} \times \textcolor{#0b5c56}{\frac{8}{7}}
Multiply. Top times top, bottom times bottom.
= \frac{3 \times 8}{5 \times 7} = \textcolor{#0b5c56}{\frac{24}{35}}
Check that it can't be simplified. 24 and 35 have no common factor other than 1, so this is the simplest form.
\text{GCF}(24, 35) = 1

All the working together

\begin{aligned} &\frac{3}{5} \div \frac{7}{8} \\[8pt]  &= \frac{3}{5} \times \frac{8}{7} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt]  &= \frac{3 \times 8}{5 \times 7} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{24}{35}}\end{aligned}

The answer in other forms

Simplest form	24/35
Decimal	0.6857142… (the 857142 repeats forever)
Percent	≈ 68.57%
Same fractions	3/5 + 7/8, 7/8 − 3/5, 3/5 × 7/8

3/5 divided by other fractions

Sum	Answer
3/5 ÷ 1/2	6/5
3/5 ÷ 1/3	9/5
3/5 ÷ 2/3	9/10
3/5 ÷ 1/4	12/5
3/5 ÷ 3/4	4/5
3/5 ÷ 1/5	3
3/5 ÷ 2/5	3/2
3/5 ÷ 4/5	3/4
3/5 ÷ 1/6	18/5
3/5 ÷ 5/6	18/25
3/5 ÷ 1/8	24/5
3/5 ÷ 3/8	8/5
3/5 ÷ 5/8	24/25
3/5 ÷ 7/8	24/35