A) Notice that the two mixed fractions are equivalent to
[tex]\begin{gathered} 4\frac{1}{3}=4+\frac{1}{3} \\ \text{and} \\ 3\frac{2}{3}=3+\frac{2}{3} \end{gathered}[/tex]
Jill transformed 4 into 12/3 and 3 into 9/3, and then she subtracted the second quantity from the first one. She forgot about the 1/3 and 2/3.
B) The correct calculation is
[tex]\begin{gathered} 4\frac{1}{3}-3\frac{2}{3}=(4+\frac{1}{3})-(3+\frac{2}{3})=4+\frac{1}{3}-3-\frac{2}{3}=(4-3)+(\frac{1}{3}-\frac{2}{3})=1+(-\frac{1}{3})=\frac{2}{3} \\ \Rightarrow4\frac{1}{3}-3\frac{2}{3}=\frac{2}{3} \end{gathered}[/tex]
The answer to part B) is 2/3
