Chapter 5 - Number Theory and the Real Number System - 5.3 The Rational Numbers - Exercise Set 5.3 - Page 285: 94

$-\dfrac{3}{4}$

Make the fractions similar using their LCD of $4$ to obtain: $$-2\frac{1}{2}+1\frac{3}{4}=-2\frac{2}{4}+1\frac{3}{4}$$ Convert each number to impropert fraction then add to obtain: \begin{align*} -2\frac{2}{4}+1\frac{3}{4}&=-\frac{4(2)+2}{4}+\frac{4(1)+3}{4}\\\\ &=-\frac{10}{4}+\frac{7}{4}\\\\ &=\frac{-10+7}{4}\\\\ &=\frac{-3}{4} \end{align*}