What Is 3/4 ÷ 7/8?

Q: What is 3/4 ÷ 7/8?

3/4 ÷ 7/8 = 6/7 (0.8571 as a decimal).

3/4 ÷ 7/8 = 6/7, about 0.857 as a decimal.

Result

Answer

\frac{3}{4} \div \frac{7}{8} = \textcolor{#0b5c56}{\frac{6}{7}}

The quotient is 6/7 in simplest form.

Decimal: \displaystyle 0.\overline{857142} (the 857142 repeats forever, about 0.8571)
Percent: 85.71%

6 of 7 equal parts

Step-by-step solution

The problem

\frac{3}{4} \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}{4}} \times \textcolor{#0b5c56}{\frac{8}{7}}
Cancel common factors. Divide 8 and 4 by 4.
= \dfrac{3}{\cancel{4}_{\,\textcolor{#0b5c56}{1}}} \times \dfrac{\cancel{8}^{\,\textcolor{#0b5c56}{2}}}{7} = \textcolor{#0b5c56}{\frac{3}{1}} \times \textcolor{#0b5c56}{\frac{2}{7}}
Multiply. Top times top, bottom times bottom.
= \frac{3 \times 2}{1 \times 7} = \textcolor{#0b5c56}{\frac{6}{7}}

All the working together

\begin{aligned} &\frac{3}{4} \div \frac{7}{8} \\[8pt]  &= \frac{3}{4} \times \frac{8}{7} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt]  &= \dfrac{3}{\cancel{4}_{\,1}} \times \dfrac{\cancel{8}^{\,2}}{7} && \textcolor{#5b6660}{\textsf{cancel}} \\[8pt]  &= \frac{3}{1} \times \frac{2}{7} \\[8pt]  &= \frac{3 \times 2}{1 \times 7} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt]  &= \textcolor{#0b5c56}{\frac{6}{7}}\end{aligned}

The answer in other forms

Simplest form	6/7
Decimal	0.857142… (the 857142 repeats forever)
Percent	≈ 85.71%
Same fractions	3/4 + 7/8, 7/8 − 3/4, 3/4 × 7/8

3/4 divided by other fractions

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