#### Answer

$\displaystyle \frac{1}{2}$

#### Work Step by Step

When dividing two numbers with like signs:
Divide their absolute values; the sign of the result is $"+"$
$\displaystyle \left(-1\frac{3}{5} \right)\div\left(-3\frac{1}{5} \right)=+\left(1\frac{3}{5} \right)\div\left(3\frac{1}{5} \right)$
Writing mixed numbers as improper fractions,
$=\displaystyle \left(\frac{8}{5} \right)\div\left(\frac{16}{5} \right)$
Dividing with a fraction $\displaystyle \frac{a}{b}$ equals multiplying with the reciprocal, $\displaystyle \frac{b}{a}$
$=\displaystyle \frac{8}{5}\cdot\frac{5}{16}$
Multiply fractions:
Reduce by the common factors, $5$ and $8$.
$=\displaystyle \frac{1}{1}\cdot\frac{1}{2}$
Now, multiply the numerators and place the product over the product of the denominators.
$=\displaystyle \frac{1}{2}$