Simplify each of the following:$\frac{1}{3}$ of $1 \frac{1}{4}+2 \frac{1}{3}$

Given:

$\frac{1}{3}$ of $1 \frac{1}{4}+2 \frac{1}{3}$

To do:

We have to simplify the given expression.

Solution:

We have to follow BODMAS rule in these types of problems.

Therefore,

$\frac{1}{3}$ of $1 \frac{1}{4}+2 \frac{1}{3}=\frac{1}{3}\times\frac{4\times1+1}{4}+\frac{3\times2+1}{3}$

$=\frac{1}{3}\times\frac{4+1}{4}+\frac{6+1}{3}$

$=\frac{1}{3}\times\frac{5}{4}+\frac{7}{3}$

$=\frac{1\times5}{3\times4}+\frac{7}{3}$

$=\frac{5}{12}+\frac{7}{3}$

$=\frac{5+7\times4}{12}$                 [LCM of 12 and 3 is 12]

$=\frac{5+28}{12}$

$=\frac{33}{12}$

Hence, $\frac{1}{3}$ of $1 \frac{1}{4}+2 \frac{1}{3}=\frac{33}{12}$.