Answer:
[tex]13\dfrac{1}{4}\ inches[/tex]
Step-by-step explanation:
To find the total length, you should add all lengths and calculate the sum. There are
3 buttons of length [tex]\frac{1}{4}[/tex] inch
2 buttons of length [tex]\frac{3}{8}[/tex] inch
4 buttons of length [tex]\frac{1}{2}[/tex] inch
2 buttons of length [tex]\frac{5}{8}[/tex] inch
3 buttons of length [tex]\frac{3}{4}[/tex] inch
2 buttons of length [tex]\frac{7}{8}[/tex] inch
2 buttons of length 1 inch
2 buttons of length [tex]1\frac{1}{4}[/tex] inches
Total length:
[tex]3\cdot \dfrac{1}{4}+2\cdot \dfrac{3}{8}+4\cdot \dfrac{1}{2}+2\cdot \dfrac{5}{8}+3\cdot \dfrac{3}{4}+2\cdot \dfrac{7}{8}+2\cdot 1+2\cdot 1\dfrac{1}{4}=\\ \\=\dfrac{3}{4}+\dfrac{3}{4}+2+\dfrac{5}{4}+\dfrac{9}{4}+\dfrac{7}{4}+2+2\cdot \dfrac{5}{4}=\\ \\=4+\dfrac{27}{4}+\dfrac{10}{4}=\\ \\=4+\dfrac{37}{4}=\\ \\=4+9\dfrac{1}{4}=\\ \\=13\dfrac{1}{4}[/tex]
