Let's break down the solution step-by-step:
1. Total Questions and Correct Answers:
- The student answered 69 questions correctly.
- The total number of questions in the exam is 100.
2. Calculate Incorrect Answers:
- To find the number of questions answered incorrectly, subtract the number of questions answered correctly from the total number of questions:
[tex]\[
\text{Incorrect Answers} = 100 - 69 = 31
\][/tex]
- So, the student answered 31 questions incorrectly.
3. Fraction of Questions Answered Incorrectly:
- To find the fraction of questions answered incorrectly, divide the number of incorrect answers by the total number of questions:
[tex]\[
\text{Fraction Incorrect} = \frac{\text{Incorrect Answers}}{\text{Total Questions}} = \frac{31}{100}
\][/tex]
- Thus, the fraction of questions answered incorrectly is [tex]\(\frac{31}{100}\)[/tex].
4. Percentage of Questions Answered Incorrectly:
- To convert the fraction to a percentage, multiply the fraction by 100:
[tex]\[
\text{Percentage Incorrect} = \left(\frac{31}{100}\right) \times 100 = 31\%
\][/tex]
- Hence, the percentage of questions answered incorrectly is 31%.
So, the detailed answers are:
- The student answered 31 questions incorrectly.
- The fraction of questions answered incorrectly is [tex]\(\frac{31}{100}\)[/tex].
- The percentage of questions answered incorrectly is [tex]\(31\%\)[/tex].
