\(30\frac12-13\frac34\)
Let's put these as improper fractions.
30 = 60/2. add the 1/2 to get 61/2
13 = 52/4. add the 3/4 to get 55/4
\(\frac{61}2-\frac{55}4\)
To add/subtract fractions, they must have the same denominator. (bottom no.)
If we multiply the top and bottom of a fraction by something, it stays equal.
We can conclude that 61/2 = 122/4. (bottom multilpies by 2, so does the top)
\(\frac{122}4-\frac{55}4\)
Now that we have a common denominator, we can subtract.
The "fourths" just sort of acts like a unit. Subtract 55 from 122 to get \(\frac{67}4\).
We can convert this to an improper fraction simply by dividing 67 by 4.
This leaves us with 16, and a remainder of 3. Our answer is \(\boxed{16\frac34}\)
