Karen colors are n squares on a grid . She colored 1/8 of the squares blue and 5/8 of the squares red . What fraction of the squares care not colored in?

Step-by-step explanation: Given that Karen colors are n squares on a grid, out of which she colored [tex]\dfrac{1}{8}[/tex] of the squares blue and [tex]\dfrac{5}{8}[/tex] of the squares red.

We are to find the fraction of the squares that are not colored.

Total number of squares = n.

Number of squares that are colored blue is given by

[tex]S_b=\dfrac{1}{8}\times n=\dfrac{n}{8},[/tex]

and the number of the squares that are colored red is given by

[tex]S_r=\dfrac{5}{8}\times n=\dfrac{5n}{8}.[/tex]

So, the total number of squares that are colored will be

[tex]SC=S_b+S_r=\dfrac{n}{8}+\dfrac{5n}{8}=\dfrac{6n}{8}=\dfrac{3n}{4}.[/tex]

Therefore, the number of squares that are not colored is

[tex]SC_n=n-\dfrac{3n}{4}=\dfrac{n}{4}=\dfrac{1}{4}\times n.[/tex]

Thus, the fraction of the squares that are not colored is [tex]\dfrac{1}{4}.[/tex]