ANSWER
She can make 19 batches of oatmeal.
EXPLANATION
First we can change the mixed number into an improper fraction:
[tex]12\frac{2}{3}=12+\frac{2}{3}=\frac{12\cdot3}{3}+\frac{2}{3}=\frac{36}{3}+\frac{2}{3}=\frac{38}{3}[/tex]
In this problem, r = 2/3. The division is:
[tex]12\frac{2}{3}\div r=\frac{38}{3}\div\frac{2}{3}[/tex]
Using the KFC rule:
[tex]\frac{38}{3}\div\frac{2}{3}=\frac{38}{3}\times\frac{3}{2}[/tex]
Solving we can see that the denominator of the first fraction can be simpliied with the numerator of the second fraction:
[tex]\frac{38}{3}\times\frac{3}{2}=\frac{38}{1}\times\frac{1}{2}=\frac{38}{2}=19[/tex]
Tyra can make 19 batches of oatmeal with 12 2/3 cups of sugar.
