What does how many times more mean in math?

"How many times" and "how many times more" are often confused.

8 is four times 2

8 is three times more than 2.

The logic underlying the second statement is as follows:

8 is 6 MORE than 2 .. .. .. .. .. .. (I)

6 is three times 2 .. .. .. .. .. .. .. (2)

Substituting for 6, from (2) into (1) gives

8 is [three times 2] more than 2

and that is collapsed (simplified) to

8 is three times more than 2.

Given any pair of positive numbers, X and Y

Y is (Y/X - 1) times more than X.