The answer is no. Not always.
There are times that the 4 digit number will involve carrying and it will be resulted into 5 digit number.
For example:
9 999 x 9, where 9 999 is a 4 digit number and 9 is a 1 digit number.
When you multiply this one, the answer will be 5 digit number.
9 999
x 9
=> 89 991, thus Joseph's statement does not apply to all multiplication process because not all 4 digit number multiplied with 1 digit number will result to 4 digit.
