Divide $2\frac{1}{5}÷1\frac{1}{5}$.

While dividing a mixed fraction by another mixed fraction, first convert the mixed fraction into an improper fraction.

We have,

$2\frac{1}{5}=\frac{11}{5}$

And, $1\frac{1}{5}=\frac{6}{5}$

Therefore,

$2\frac{1}{5}÷1\frac{1}{5}$

$=\frac{11}{5}÷\frac{6}{5}$

$=\frac{11}{5}\times \mathrm{reciprocal} \mathrm{of} \frac{6}{5}$

$=\frac{11}{5}\times \frac{5}{6}$

$=\frac{11\times 5}{5\times 6}$

$=\frac{11}{6}$

$=1\frac{5}{6}$