Theory:

  • 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 43 by 27, we multiply the reciprocal of 27 and obtain the result.      
 
43÷27=43×72=43×72=286=143
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.