Chapter 1 - Introduction to Algebraic Expressions - 1.5 Addition of Real Numbers - 1.5 Exercise Set - Page 42: 54

$\frac{5}{26}$

To add two numbers with different signs, we subtract their absolute values ($\frac{1}{2} - \frac{4}{13} = \frac{13}{26} - \frac{8}{26} = \frac{5}{26}$) and take the sign of the larger absolute value, which is positive.