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 butto…

Question

asked Dec 21, 2020 125k views

1 Answer

Prasad Bhosale · Answer 1 · 2020-12-24T17:34:08+0000

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.