The first picture about the rational numbers I am not sure the answer.
In the second picture the set that are all equivalent to the fraction is the second set.
In the third picture
the equivalent expression is the first one.
In the fourth picture the correct situation is the first one about buying popcorn.
Hope this helps a little, sorry I could not help more.
No. We claim that

and use algebra to prove the statement.
Let

. Multiply this by ten to get

. Subtract the initial equation to give

and divide by

to see that

. Substituting into the original equation gives

, proving the desired statement.
1 is 117 because 18x6.5 is 117