Let's analyze Jessie’s work step by step to identify the errors.
a. Find and describe Jessie’s error.
- Initial Division: Jessie starts with \(325 \div 310\). This is the correct initial operation, but Jessie appears to incorrectly transition to another division.
- Incorrect Transition: Instead of proceeding correctly with the division, Jessie writes \(175 \div 310\). It is unclear how this transition is made as it doesn't seem related to \(325 \div 310\).
- Multiplication: After writing \(175 \div 310\), Jessie then writes \(175 \cdot 310\). This is a completely incorrect operation since multiplying does not solve the original division problem.
- Factoring: Later, Jessie breaks down \(175\) into \(17 \cdot 35 \cdot 10\), but this is irrelevant to the division problem and does not help in finding an answer to \(325 \div 310\).
- Final Incorrect Answer: Ultimately, Jessie concludes with \(5150 = 1150\), but this equation is also not valid in the context of the division problem.
Overall, Jessie's error lies in not following the correct process for division and introducing irrelevant calculations.
b. What is the correct answer?
To find the correct answer to \(325 \div 310\):
- Perform the Division:
\[ 325 \div 310 \approx 1.04838709677 \] However, to express this as a common fraction, we can simplify it further: \[ \frac{325}{310} = \frac{65}{62} \text{ (after dividing both by 5)} \]
Thus, the correct answer can be approximately \(1.048\) or it can be expressed as the simplified fraction \( \frac{65}{62} \). In decimal form, the answer is approximately 1.05 (when rounded to two decimal places).