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