Find the value of $ 1 \frac{1}{4}+3 \frac{1}{2} $.

Given:

\( 1 \frac{1}{4}+3 \frac{1}{2} \).

To do:

We have to find the value of \( 1 \frac{1}{4}+3 \frac{1}{2} \).

Solution:

$1\frac{1}{4}+3\frac{1}{2}=\frac{1\times4+1}{4}+\frac{3\times2+1}{2}$

$=\frac{4+1}{4}+\frac{6+1}{2}$

$=\frac{5}{4}+\frac{7}{2}$

$=\frac{5+7\times2}{4}$     (LCM of 2 and 4 is 4) 

$=\frac{5+14}{4}$

$=\frac{19}{4}$

Therefore,

$1\frac{1}{4}+3\frac{1}{2}=\frac{19}{4}$.