To obtain the measure of segment AD, add the measurement of segment AC and segment CD.
[tex]AD=AC+CD=2\frac{3}{8}+1\frac{1}{4}[/tex]
Rewrite the fraction part as similar fractions. Multiply the numerator and teh denominator of the second fraction by 2 to obtain 8 in the denominator.
[tex]\begin{gathered} AC+CD=2\frac{3}{8}+1\frac{1\cdot2}{4\cdot2} \\ =2\frac{3}{8}+1\frac{2}{8} \end{gathered}[/tex]
Add the whole numbers, 2 and 1. Add the numerators, 3 and 2, and then copy the common denominator, which is 8.
[tex]\begin{gathered} AD=2\frac{3}{8}+1\frac{2}{8} \\ =3\frac{5}{8}_{} \end{gathered}[/tex]
Therefore, the correct answer is the third option, 3 5/8 in.
