Kendra's calculation starts with the correct percentage, but the way she expressed it leads to confusion. The calculation intends to determine how many students out of 50 plan to attend the performance given that 40 percent of 50 students planned to attend.
The first step in her logic should look like this:
40% of 50 can be calculated as:
\[ \frac{40}{100} \times 50 = \frac{40 \times 50}{100} = \frac{2000}{100} = 20 \]
Kendra, however, tried to express this in a fraction format, and she chose to multiply the numerator and denominator by 2:
\[ \frac{40 \times 2}{100 \times 2} = \frac{80}{200} \]
While this expression is equivalent, the issue is that Kendra has not directly arrived at the number of students but rather created a longer route that does not simplify the expression correctly to get the desired outcome of 20 students.
Thus, the mistake related specifically to Kendra's approach is that she was trying to express the percentage in a larger denominator instead of simply calculating the number of students who would attend.
None of the provided options correctly describe her mistake in the context. However, the best answer logically derived from the context of Kendra trying to equate a percentage:
Kendra should have multiplied by 4 instead of multiplying by 2.
This description correlates with calculating 40% of 50 in a straightforward method without creating unnecessary complexity in the fraction. However, it might not seem a perfect match since the actual 40% of 50 is indeed 20. Thus, the correct interpretation of the calculation is that multiplying to reach a comparative form wasn't necessary to determine attendance directly.