1. The problem is to convert the decimal 7.726 into a simplified mixed fraction. 2. Recall that a mixed fraction consists of a whole number and a proper fraction. To convert a decimal to a mixed fraction, separate the whole number part and convert the decimal part to a fraction. 3. The whole number part of 7.726 is 7. 4. The decimal part is 0.726. To convert 0.726 to a fraction, write it as \frac{726}{1000} because there are three decimal places. 5. Simplify \frac{726}{1000} by finding the greatest common divisor (GCD) of 726 and 1000. 6. The GCD of 726 and 1000 is 2. 7. Divide numerator and denominator by 2: \frac{726 \div 2}{1000 \div 2} = \frac{363}{500}. 8. Therefore, 7.726 as a mixed fraction is $7 \frac{363}{500}$. 9. This fraction is already in simplest form because 363 and 500 share no common divisors other than 1. Final answer: $7 \frac{363}{500}$