1. The problem asks for the range of the three fractions: $\frac{7}{10}$, $\frac{19}{30}$, and $\frac{7}{9}$. The range is the difference between the largest and smallest values. 2. First, convert each fraction to decimal form to compare them easily: $$\frac{7}{10} = 0.7$$ $$\frac{19}{30} = \frac{19}{30} \approx 0.6333$$ $$\frac{7}{9} = \frac{7}{9} \approx 0.7777$$ 3. Identify the smallest and largest fractions: - Smallest: $\frac{19}{30} \approx 0.6333$ - Largest: $\frac{7}{9} \approx 0.7777$ 4. Calculate the range by subtracting the smallest from the largest: $$\text{Range} = \frac{7}{9} - \frac{19}{30}$$ 5. Find a common denominator to subtract the fractions. The least common denominator (LCD) of 9 and 30 is 90. Convert each fraction: $$\frac{7}{9} = \frac{7 \times 10}{9 \times 10} = \frac{70}{90}$$ $$\frac{19}{30} = \frac{19 \times 3}{30 \times 3} = \frac{57}{90}$$ 6. Subtract the fractions: $$\frac{70}{90} - \frac{57}{90} = \frac{70 - 57}{90} = \frac{13}{90}$$ 7. The fraction $\frac{13}{90}$ is already in simplest form because 13 is a prime number and does not divide 90. **Final answer:** The range of the three fractions is $\boxed{\frac{13}{90}}$.