Answer: The fraction of the squares that are not colored is \(\dfrac{1}{4}.\)
Step-by-step explanation: Given that Karen colors are n squares on a grid, out of which she colored \(\dfrac{1}{8}\) of the squares blue and \(\dfrac{5}{8}\) 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
\(S_b=\dfrac{1}{8}\times n=\dfrac{n}{8},\)
and the number of the squares that are colored red is given by
\(S_r=\dfrac{5}{8}\times n=\dfrac{5n}{8}.\)
So, the total number of squares that are colored will be
\(SC=S_b+S_r=\dfrac{n}{8}+\dfrac{5n}{8}=\dfrac{6n}{8}=\dfrac{3n}{4}.\)
Therefore, the number of squares that are not colored is
\(SC_n=n-\dfrac{3n}{4}=\dfrac{n}{4}=\dfrac{1}{4}\times n.\)
Thus, the fraction of the squares that are not colored is \(\dfrac{1}{4}.\)
