No, because ...
For every division problem, there is a corresponding multiplication problem.
Example: 6 ÷ 2 = 3 because 2 x 3 = 6.
Example: 27 ÷ -3 = -9 because -3 x -9 = 27.
However, try 10 ÷ 0 = ? To get an answer to this problem, there must be a number so that 0 x that number = 10. There isn't a number that works.
One strange case: what is 0 ÷ 0 = ?. This is different, because you can replace the question mark with every number: 0 x 0 = 0, 0 x 1 = 0, 0 x 2 = 0, etc. There is no answer in this case because every number works.