Answer
$ a.\quad$Improper fraction:$\displaystyle \quad\frac{4}{3} .$
$ b.\quad$Mixed number:$\displaystyle \quad 1\frac{1}{3}$
Work Step by Step
Each object is divided into 3 equal parts.
Each part represents $\displaystyle \frac{1}{3}$ of the object.
Four parts in all are shaded, or $\displaystyle \frac{4}{3}$.
As a mixed number, we have 1 whole object and $\displaystyle \frac{1}{3}$ of the second one...or, $1\displaystyle \frac{1}{3}$ .
( Dividing $4\div 3$, quotient = $1$, remainder $1,$ so $\displaystyle \frac{4}{3}=1\frac{1}{3}$ )
