Nate operates a hot dog stand. on wednesday he used 5 bags of hot dog
buns. on thursday he used 1 3/4 times as many hot dog buns as on
wednesday. how many bags of hot dog buns did nate use on thursday?
simplify your answer and write it as a proper fraction or as a whole or mixed number.

When you read this, you immediately get this feeling that the answer is
(1 and 3/4) times (5) .  The only problem is that it's kind of messy to
try and do the multiplication with (1 and 3/4) in that form, so it's a lot
easier if you change it to a different form ... you don't change the value
of the number, you just write it differently.

In place of (1 and 3/4), you could use  1.75 , or you could use  7/4 .
They're both exactly the same amount as (1 and 3/4), but they look
different, and they're easier to work with.

Since the problem wants the answer as a fraction or mixed number,
let's use  7/4  in place of  (1 and 3/4).

OK.  Five bags were used on Thursday, and (7/4) of that many were used
on Friday.

(7/4) x (5 bags) = 35/4 bags . . . . . That's the improper fraction.

The mixed number is  (8 and 3/4) bags.