Alright, let’s tackle the problem step-by-step.
1. Understand the given information:
- The student had homework for 67 days out of a total of 100 days.
- We need to determine the fraction and percentage of days the student did not have homework.
2. Calculate the number of days the student did not have homework:
[tex]\[
\text{Days without homework} = \text{Total days} - \text{Homework days} = 100 - 67 = 33 \text{ days}
\][/tex]
3. Find the fraction of days without homework:
[tex]\[
\text{Fraction of days without homework} = \frac{\text{Days without homework}}{\text{Total days}} = \frac{33}{100}
\][/tex]
Therefore, the fraction of days without homework is \(\frac{33}{100}\), which corresponds to option F.
4. Calculate the percentage of days without homework:
[tex]\[
\text{Percentage of days without homework} = \left(\frac{\text{Days without homework}}{\text{Total days}}\right) \times 100 = \left(\frac{33}{100}\right) \times 100 = 33 \%
\][/tex]
Therefore, the percentage of days without homework is \(33\%\), which corresponds to option A.
5. Summary:
- Fraction of days without homework: \(\frac{33}{100}\) (option F)
- Percentage of days without homework: \(33\%\) (option A)
So, the correct answers are:
A. \(33 \%\)
F. [tex]\(\frac{33}{100}\)[/tex]
