Question

Find the value of

$2\frac{1}{3}-(-1\frac{1}{3}-3\frac{1}{3}+\frac{1}{2})-\frac{2}{3}$

Answer 1

Finding the value of given expression

To solve this first convert the given mix fraction into improper fraction.

$2\frac{1}{3}=\frac{7}{3}$ [first multiply $3$by $2$ and then add$1$]

$1\frac{1}{3}=\frac{4}{3},3\frac{1}{3}=\frac{10}{3}$

According to the BODMAS, first solve the bracket and then the other part

$\begin{array}{rcl}\left(-1\frac{1}{3}-3\frac{1}{3}+\frac{1}{2}\right)& =& -\frac{4}{3}-\frac{10}{3}+\frac{1}{2}\\ & =& -\frac{14}{3}+\frac{1}{2}\\ & =& \frac{-28+3}{6}\\ & =& \frac{-25}{6}\end{array}$ [LCM of $(2,3)$ is $6$]

Now,

$\begin{array}{rcl}2\frac{1}{3}-\left(1\frac{1}{3}-3\frac{1}{3}+\frac{1}{2}\right)-\frac{2}{3}& =& 2\frac{1}{3}-\left(-\frac{25}{6}\right)-\frac{2}{3}\\ & =& \frac{7}{3}+\frac{25}{6}-\frac{2}{3}\\ & =& \frac{14+25-4}{6}\\ & =& \frac{39-4}{6}\\ & =& \frac{35}{6}\end{array}$[LCM of $(3,6)$ is $6$ ]

Hence, the value of given expression is $\frac{35}{6}$