Elementary Technical Mathematics

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