You have two buttons of different lengths.
First with length [tex]1\dfrac{1}{4}[/tex] in and second with length [tex]\dfrac{3}{8}[/tex] in. The first one is larger, then the difference in length between them is:
[tex]1\dfrac{1}{2}-\dfrac{3}{8}=\dfrac{3}{2}-\dfrac{3}{8}=\dfrac{3\cdot 4-3}{8}=\dfrac{12-3}{8}=\dfrac{9}{8}=1\dfrac{1}{8}\ in.[/tex]
Answer: [tex]1\dfrac{1}{8}[/tex] in.
