How do you convert improper fractions to mixed numbers and mixed numbers to improper fractions

For example let's say I want to convert 19/6 to a mixed number. For converting this improper fraction to a mixed number, I would want to divide 19 by 6 to get my mixed number which would be 3 with a remainder of 1. That one becomes a fration with 6 as the denominater since the improper fraction had a denominater of 6. For converting mixed numbers, (using the one we coverted from the improper fraction), I would times the whole number (in this equation 3) by the factions denominater (6) which equals 18. Then I would add the 1 from the fraction to get my improper fraction which is 19/6.