Answer
\frac{7}{8} \div \frac{2}{5} = \textcolor{#0b5c56}{\frac{35}{16} = 2\frac{3}{16}}
The quotient is 35/16 in simplest form, or 2 3/16 as a mixed number.
Decimal: \displaystyle 2.1875 Percent: 218.75% 2 wholes + 3 of 16 equal parts
Step-by-step solution The problem
\frac{7}{8} \div \frac{2}{5}
Flip \displaystyle \frac{2}{5} Dividing by a fraction is the same as multiplying by its reciprocal (the fraction turned upside down).
\frac{2}{5} \;\rightarrow\; \frac{5}{2}
= \textcolor{#0b5c56}{\frac{7}{8}} \times \textcolor{#0b5c56}{\frac{5}{2}}
Multiply. Top times top, bottom times bottom.
= \frac{7 \times 5}{8 \times 2} = \textcolor{#0b5c56}{\frac{35}{16}}
Check that it can't be simplified. 35 and 16 have no common factor other than 1, so this is the simplest form.
\text{GCF}(35, 16) = 1
Write it as a mixed number. Divide: 16 goes into 35 2 times with 3 left over. The whole number is 2, the remainder 3 becomes the numerator, and the denominator stays 16.
35 \div 16 = 2\ \text{R}\ 3
= \textcolor{#0b5c56}{2\frac{3}{16}}
All the working together \begin{aligned} &\frac{7}{8} \div \frac{2}{5} \\[8pt] &= \frac{7}{8} \times \frac{5}{2} && \textcolor{#5b6660}{\textsf{flip}} \\[8pt] &= \frac{7 \times 5}{8 \times 2} && \textcolor{#5b6660}{\textsf{multiply}} \\[8pt] &= \frac{35}{16} \\[8pt] &= \textcolor{#0b5c56}{2\frac{3}{16}} && \textcolor{#5b6660}{\textsf{mixed number}}\end{aligned}