Add

$-\frac{17}{4}$

Explanation

We will write -5 as the fraction \(\frac{-5}{1}\).  Then we will follow the steps for adding fractions that have different denominators.  The fraction \(\frac{-5}{1}\) and \(\frac34\) have different denominators.

Since the smallest number the denominators 1 and 4 divide exactly is 4, the LCD is 4

Write -5 as \(\frac{-5}{1}\)

$-5 + \frac34 = \frac{-5}{1} + \frac34$

To build \(\frac{-5}{1}\) so that its denominator is 4, multiply it by a form of 1

$= \frac{-5}{1} \color{red}{ \cdot \frac44} + \frac34$

Multiply the numerators.  Multiply the denominators.  The denominators are now the same.

$= \frac{-20 + 3}{4}$

Use the rule for adding two integers with different signs: -20 + 3 = -17

$= \frac{-17}{4}$

Write the result with - sign in front: \(\frac{-17}{4} = - \frac{17}{4}\).  This fraction is in simplest form

$= -\frac{17}{4}$