a. Jessie's error occurs in the step where she converts the division of fractions into multiplication. The proper method to divide fractions is to multiply by the reciprocal of the second fraction. In Jessie's work, she seems to have incorrectly simplified \( \frac{3}{25} \div \frac{3}{10} \) as \( \frac{17}{5} \div \frac{3}{10} \), which is a significant mistake and leads her to an erroneous conclusion.
The correct operation should be: \[ \frac{3}{25} \div \frac{3}{10} = \frac{3}{25} \times \frac{10}{3} \] Instead of transforming it to \( \frac{17}{5} \div \frac{3}{10} \).
b. To find the correct answer, we should multiply \( \frac{3}{25} \) by the reciprocal of \( \frac{3}{10} \): \[ \frac{3}{25} \times \frac{10}{3} \]
When we multiply:
- Multiply the numerators: \( 3 \times 10 = 30 \)
- Multiply the denominators: \( 25 \times 3 = 75 \)
Putting it all together: \[ \frac{30}{75} \]
Now we simplify \( \frac{30}{75} \) by dividing both the numerator and the denominator by 15: \[ \frac{30 \div 15}{75 \div 15} = \frac{2}{5} \]
Thus, the correct answer is: \[ \frac{2}{5} \]