evaluate the expression. simplify if possible. 3\\frac{1}{2}+(-8\\frac{3}{4})

Explanation:

Step1: Convert mixed - numbers to improper fractions

$3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2}$ and $- 8\frac{3}{4}=-\frac{8\times4+3}{4}=-\frac{35}{4}$

Step2: Find a common denominator

The common denominator of 2 and 4 is 4. So, $\frac{7}{2}=\frac{7\times2}{2\times2}=\frac{14}{4}$

Step3: Add the fractions

$\frac{14}{4}+(-\frac{35}{4})=\frac{14 - 35}{4}=\frac{-21}{4}$

Step4: Convert back to mixed - number

$\frac{-21}{4}=- 5\frac{1}{4}$

Answer:

$-5\frac{1}{4}$