19 ½ – 13 ¼=

The quick way to answer this is to observe that 1/4 is being subtracted from 1/2.  Since 1/4 + 1/4 = 1/2, 1/2 - 1/4 = 1/4. So treat the fractions as a separate subtraction.  Then you're left with 19 - 13, which is 6.  So your answer is 6 1/4.

The more formal way to do this is to multiply the denominator with the whole number, and add the result to the numerator to make a new fraction:

19 * 2 = 38 + 1 = 39,  or 39/2

Do the same with the other number

13 * 4 = 52 + 1 = 52, or 53/4

Now you need to subtract these two new fractions, but in order to do that, the denominators have to be the same, so we'll multiply 39/2 *2 to make 78/4

Now you can subtract 78/4 - 53/4 = 25/4 = 6.25