Respuesta :
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
[tex]\frac{1}{8}\ inch[/tex]
Size of second button is given by
[tex]\frac{3}{8}\ inch[/tex]
Size of third button is given by
[tex]\frac{1}{4}\ inch[/tex]
The size of hole of the shirt is given by
[tex]\frac{2}{6}\ inch=\frac{1}{3}\ inch[/tex]
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
[tex]\frac{1}{8}\ inch=\frac{1\times 3}{8\times 3}=\frac{3}{24}\ inch[/tex]
Similarly, Size of second button is given by
[tex]\frac{3}{8}\ inch=\frac{3\times 3}{8\times 3}=\frac{9}{24}\ inch[/tex]
Similarly, Size of third button is given by
[tex]\frac{1}{4}\ inch=\frac{1\times 6}{4\times 6}=\frac{6}{24}\ inch[/tex]
And, The size of hole of the shirt is given by
[tex]\frac{1}{3}\ inch=\frac{1\times 8}{3\times 8}=\frac{8}{24}[/tex]
As we can see that
[tex]\frac{3}{24}<\frac{8}{24}\\\\and\\\\\frac{6}{24}<\frac{8}{24}[/tex]
Hence, the first and last button will fit through the button hole.
