Converting fractional units into mixed units

We now present two different methods for unwrapping a fractional part into mixed units.

Suppose now that we wish to convert ${\displaystyle 5\frac{7}{9}}$ yards into yard, feet, and inches.

In the first method, we proceed by splitting into whole and fractional parts, and rewriting the fractional part in smaller units, e.g






In the second method, we first multiply ${\displaystyle 5\frac{7}{9}}$,  by ${\displaystyle 3}$ and by ${\displaystyle 12}$, to get ${\displaystyle 208}$, and then we use successive division as in the last posting.  We can even shorten this method by extracting the ${\displaystyle 5}$ first, multiplying just the ${\displaystyle \frac{7}{9}}$ by ${\displaystyle 3}$ and by ${\displaystyle 12}$ to get ${\displaystyle 28}$, and then dividing as before; this spares us the last division : ${\displaystyle 28 = 2_{12}4.}$