Theory:

Multiplication of rational numbers is similar to the multiplication of integers.
  • All we have to do is multiply the numerator and the denominators by the given numbers.
  • Thus we can say that the product of rational numbers is the ratio of multiplication of numerators and denominators.
Example:
The following result is obtained by multiplying the numerators and the denominators.
 
24×37=2×34×7=628
If the product has an even number of negative multipliers, then the multiplication is positive, because the product of two negative numbers is a positive number.
 
If the product has an odd number of negative multipliers, then the product is negative.
Example:
  • 6×4×2=48 (multiplies by two negative numbers - even number).
  • 6×4×1×2=48 (multiplies by three negative numbers - odd number).
     
  • 1×1×13×13=19
     
  • 1×0.2×1×0.2×1=0.04
This law also applies to division or division and multiplication together.
 
For instance, 2:1×6×5:2=30
 
The operations shall be carried out successively, resulting in a minus sign (\(-\)) because there are three negative numbers.