Question

Lola measures three buttons for a shirt she is making. one button is 1/8 inch, one is 3/8 inch, and one is 1/4 inch. the button hole on the shirt is 2/6 inch. which of the buttons will fit through the button hole ? explain

Answer 1

Answer: The first and last button will fit through the button hole.

Explanation:

since we have given that

Size of first button is given by

`(1)/(8)\ inch`

Size of second button is given by

`(3)/(8)\ inch`

Size of third button is given by

`(1)/(4)\ inch`

The size of hole of the shirt is given by

`(2)/(6)\ inch=(1)/(3)\ inch`

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

`(1)/(8)\ inch=(1* 3)/(8* 3)=(3)/(24)\ inch`

Similarly, Size of second button is given by

`(3)/(8)\ inch=(3* 3)/(8* 3)=(9)/(24)\ inch`

Similarly, Size of third button is given by

`(1)/(4)\ inch=(1* 6)/(4* 6)=(6)/(24)\ inch`

And, The size of hole of the shirt is given by

`(1)/(3)\ inch=(1* 8)/(3* 8)=(8)/(24)`

As we can see that

`(3)/(24)<(8)/(24)\\\\and\\\\(6)/(24)<(8)/(24)`

Hence, the first and last button will fit through the button hole.