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.