Given:
The expression is
[tex]2\dfrac{1}{3}-1\dfrac{2}{5}[/tex]
To find:
The error in Frankie's work.
Solution:
We need to simplify [tex]2\dfrac{1}{3}-1\dfrac{2}{5}[/tex], so
[tex]2\dfrac{1}{3}=2\dfrac{1}{3}\times \dfrac{5}{5}[/tex]
[tex]2\dfrac{1}{3}=2\dfrac{5}{15}[/tex]
and,
[tex]1\dfrac{2}{5}=-1\dfrac{2}{5}\times \dfrac{3}{3}[/tex]
[tex]1\dfrac{2}{5}=-1\dfrac{6}{15}[/tex]
Now,
[tex]2\dfrac{1}{3}-1\dfrac{2}{5}=2\dfrac{5}{15}-1\dfrac{6}{15}[/tex]
[tex]2\dfrac{1}{3}-1\dfrac{2}{5}=(2+\dfrac{5}{15})-(1+\dfrac{6}{15})[/tex]
[tex]2\dfrac{1}{3}-1\dfrac{2}{5}=2+\dfrac{5}{15}-1-\dfrac{6}{15}[/tex]
[tex]2\dfrac{1}{3}-1\dfrac{2}{5}=1-\dfrac{1}{15}[/tex]
[tex]2\dfrac{1}{3}-1\dfrac{2}{5}=\dfrac{14}{15}[/tex]
Therefore, there is error in Frankie's last step. In that step, he did not subtract the mixed fraction correctly.