Final answer:
To reduce the mixed number 4(11)/(66) to lowest terms, divide the numerator and denominator by their greatest common factor which is 11. The reduced fraction is 1/6, so the mixed number is 4 1/6.
Step-by-step explanation:
To reduce the mixed number 4(11/66) to its lowest terms, you first need to divide both the numerator and the denominator of the fraction by their greatest common divisor (GCD). In this case, the GCD of 11 and 66 is 11. Therefore, divide 11 by 11 to get 1, and 66 by 11 to get 6, simplifying the fraction to 1/6.
Next, you integrate the whole number with the simplified fraction. The mixed number becomes 4 1/6.