### Theory:

Division of the Rational Number
Division of the Rational number is done by multiplying the reciprocal of the number to be divided. It is similar to divisions of fractions.
Example:
For dividing $\frac{4}{3}\phantom{\rule{0.147em}{0ex}}\mathit{by}\phantom{\rule{0.147em}{0ex}}\frac{2}{7}$, we multiply the reciprocal of $\frac{2}{7}$ and obtain the result.

$\begin{array}{l}\frac{4}{3}÷\frac{2}{7}=\frac{4}{3}×\frac{7}{2}\\ =\frac{4}{3}×\frac{7}{2}\\ =\frac{28}{6}\\ =\frac{14}{3}\end{array}$

The resultant answer is the ratio of the product of the numerators and the product of the denominators.
To divide two rational numbers, divide their modules, i.e. only the digits. Then determine the sign of the result.
Let us recollect the basic division principles:
A division is a positive number if the divisor and the dividend have equal signs:
$$(+):(+) = (+)$$
$$( - ):( - ) = (+)$$

A division is a negative number if the divisor and the dividend have different characters:
$$(+):( - ) = ( - )$$
$$( - ):(+) = ( - )$$
Example:
1. $$(-16):(-4) = + (|-16|:|-4|) = + (16:4) = 4$$

2. $$16:(-4) = - (|16| : |-4|) = - (16:4) = -4$$

3. $$0 :(- 3) = 0$$ (Zero divided by any number is always zero).

4. $$(- 3) : 0$$ cannot be performed.
When solving the examples, we may not write the module marks, but the result can be calculated immediately by cognitive thinking:
$$-30:( - 6) = + 5 = 5$$
$$-30 : 30 = - 1$$