The expression "4 whole 4 over 1" can be interpreted as the mixed number 4 \( \frac{4}{1} \).
When converting this to an improper fraction, you would multiply the whole number by the denominator and then add the numerator:
\[ 4 \times 1 + 4 = 4 + 4 = 8 \]
So, the mixed number 4 \( \frac{4}{1} \) can be expressed as the improper fraction:
\[ \frac{8}{1} \]
In simplest terms, this is simply 8.