NOD to the QROD - a mnemonic for converting improper fractions

I was trying to think of how to teach my kids about converting improper fractions to mixed form. The whole process is kind of confusing and easy to forget. I came up with the following mnemonic to help remember how to do it:

NOD to QROD

What does that mean? It sounds like a mantra that fans might chant at a baseball game as their favorite baseball star QROD approaches the plate. "NOD to QROD, NOD to QROD, NOD to QROD"... Then QROD goes up to the plate, here's the pitch... it's a long drive deep to center field, it's going, it's going, it's gone. QROD hits a home run! Everybody in the park explodes with excitement as QROD circles the bases.

So with NOD to QROD, you can hit a home run every time you want to convert an improper fraction. So again, what does that mean?

Numerator Over Denominator to Quotient Remainder Over Denominator

You always start with an improper fraction of the form Numerator Over Denominator. Your goal is to convert the fraction into mixed form. What that really means is that you should express the fraction as Quotient Remainder Over Denominator. For example suppose you wanted to convert the improper fraction 37/5 into mixed form. Reading the expression out loud we have "37 Over 5". The Numerator 37 is Over the Denominator 5. As I'll explain in the next paragraph, you'll need to do some long division and get a Quotient 7 and Remainder 2. Using the mnemonic, we need to write the answer as QROD. So Quotient 7 Remainder 2 Over Denominator 5 or 7 2/5. Summarizing:

N O D to Q R O D

37/ 5 = 7 2/5

So that tells you how to write the final answer, but it doesn't tell you how to get Q the quotient, or R the remainder. For that you'll need to know how to do long division, something that you will need to learn to do first. But once you know how to do long division, the Quotient is what you get on top, and the Remainder is what you get at the very end, when you've finished dividing the numerator as much as possible into the denominator. For example, the 37/5 example, you would do something like

      7    ---------Quotient

   _______

 5 | 3 7  

     3 5    

     ---

       2    --------Remainder 

Or in general:

                    Q   Quotient

                _______

 Denominator D |   N    Numerator    

                   .

                     .

                       .  

                         R  Remainder

so visually the NOD to QROD means:

                ___Q___

N/D     =    D |   N         =   Q  R/D     

                    ... R