Does multiplication always make things bigger?

Answer 1

This is a pretty technical question. The answer will vary depending on your grade level.

If you are talking about magnitude (i.e., ignore the negative) than the answer is sort of (I'll explain further down).

If you are allowing negative numbers,

Start with 2, and multiply it by -1. 2 x -1 = -2 which is smaller than 2.

Now, what about multiplying by a number between 0 and 1 (0.5 for example).

Start with 4 and multiply by .5 to get 2. 2 is smaller than 4.

However, you could argue that by multiplying by a decimal, you are in addition to multiplying, dividing which is why the number is reduced. By the same logic, division would always result in a number of lower magnitude. That would be the side I would tend to take as well, so:

Multiplication always increases the magnitude of a number, but does notnecessarilymake it bigger. Division always reduces the magnitude of a number, but does not necessarily make it larger.

I should also mention, this is controversial. People can make the argument either way (in regards to multiplication vs division).