Answer: The first and last button will fit through the button hole.
Step-by-step explanation:
since we have given that
Size of first button is given by
![\frac{1}{8}\ inch](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D%5C%20inch)
Size of second button is given by
![\frac{3}{8}\ inch](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B8%7D%5C%20inch)
Size of third button is given by
![\frac{1}{4}\ inch](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%5C%20inch)
The size of hole of the shirt is given by
![\frac{2}{6}\ inch=\frac{1}{3}\ inch](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B6%7D%5C%20inch%3D%5Cfrac%7B1%7D%7B3%7D%5C%20inch)
So, the size of button must be smaller than the size of hole in the shirt to get fit .
Since we first make the denominator same , as L.C.M. of all denominators i.e.(8,8,4,and 3) is 24
So, Size of first button is given by
![\frac{1}{8}\ inch=\frac{1\times 3}{8\times 3}=\frac{3}{24}\ inch](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D%5C%20inch%3D%5Cfrac%7B1%5Ctimes%203%7D%7B8%5Ctimes%203%7D%3D%5Cfrac%7B3%7D%7B24%7D%5C%20inch)
Similarly, Size of second button is given by
![\frac{3}{8}\ inch=\frac{3\times 3}{8\times 3}=\frac{9}{24}\ inch](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B8%7D%5C%20inch%3D%5Cfrac%7B3%5Ctimes%203%7D%7B8%5Ctimes%203%7D%3D%5Cfrac%7B9%7D%7B24%7D%5C%20inch)
Similarly, Size of third button is given by
![\frac{1}{4}\ inch=\frac{1\times 6}{4\times 6}=\frac{6}{24}\ inch](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%5C%20inch%3D%5Cfrac%7B1%5Ctimes%206%7D%7B4%5Ctimes%206%7D%3D%5Cfrac%7B6%7D%7B24%7D%5C%20inch)
And, The size of hole of the shirt is given by
![\frac{1}{3}\ inch=\frac{1\times 8}{3\times 8}=\frac{8}{24}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5C%20inch%3D%5Cfrac%7B1%5Ctimes%208%7D%7B3%5Ctimes%208%7D%3D%5Cfrac%7B8%7D%7B24%7D)
As we can see that
![\frac{3}{24}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B24%7D%3C%5Cfrac%7B8%7D%7B24%7D%5C%5C%5C%5Cand%5C%5C%5C%5C%5Cfrac%7B6%7D%7B24%7D%3C%5Cfrac%7B8%7D%7B24%7D)
Hence, the first and last button will fit through the button hole.