What are there different improper fractions that equal 4 1/2

Well 4 just means that there are 4 of these things. so 1/2 is also the same as 50/100 or 25/50  or 500/1000 (the gist of it) so you just multiply the bottom and the top by the same number which would just give you different improper fractions

4 1/2 is equal to:
9/2
18/4
36/8

You get the first one by taking the 4, multiplying it by the denominator, in this case 2, and adding that to the top. So you end up with 9/2. Then you can double that, what you get, in this case 18/4, is equal to the one before that. You could keep doubling it forever and ever and ever and it would still be equal to 4 1/2.

Hope this helps!

Absolute value graph shifted point 5 up