1. The problem is to calculate the value of $q := 27 \div 33$. 2. Division is the operation of determining how many times one number is contained within another. Here, we divide 27 by 33. 3. The formula for division is: $$q = \frac{27}{33}$$ 4. Simplify the fraction by finding the greatest common divisor (GCD) of 27 and 33. - The factors of 27 are 1, 3, 9, 27. - The factors of 33 are 1, 3, 11, 33. - The GCD is 3. 5. Divide numerator and denominator by 3: $$q = \frac{27 \div 3}{33 \div 3} = \frac{9}{11}$$ 6. The fraction $\frac{9}{11}$ cannot be simplified further. 7. To express as a decimal, divide 9 by 11: $$9 \div 11 \approx 0.8181$$ (rounded to four decimal places). 8. Therefore, the value of $q$ is $\frac{9}{11}$ or approximately 0.8181.