Question

in kendra’s class, 40 percent of the students earned an a on the math test. twenty students earned an a. kendra needs to find out how many students are in her class. kendra’s work is shown below.
\\(\frac{\text{part}}{\text{whole}} = \frac{40\div2}{100\times2} = \frac{20}{200}\\)

what mistake did kendra make?

\\(\circ\\) kendra should have multiplied by 4 in both the numerator and the denominator.
\\(\circ\\) kendra should have divided by 2 instead of multiplying by 2 in the denominator.
\\(\circ\\) kendra should have added 40 and 20.
\\(\circ\\) kendra should have the part to whole equation written as \\(\frac{100}{40}\\).

Explanation:

Step1: Recall percentage formula

The formula for percentage is \(\frac{\text{part}}{\text{whole}}=\frac{\text{percentage}}{100}\). Here, part \( = 20\), percentage \( = 40\), so \(\frac{20}{\text{whole}}=\frac{40}{100}\).

Step2: Analyze Kendra's work

Kendra did \(\frac{40\div2}{100\times2}=\frac{20}{200}\), which is incorrect. Let's solve the correct equation: \(\text{whole}=\frac{20\times100}{40}=50\). Now, let's check each option:

• Option 1: Multiplying by 4 in numerator and denominator: \(\frac{40\times4}{100\times4}=\frac{160}{400}\), not relevant.
• Option 2: Dividing denominator by 2: \(\frac{40\div2}{100\div2}=\frac{20}{50}\), which gives whole \( = 50\), correct approach.
• Option 3: Adding 40 and 20 is wrong as per percentage formula.
• Option 4: Writing as \(\frac{100}{40}\) is not the correct part - whole setup.

Answer:

Kendra should have divided by 2 instead of multiplying by 2 in the denominator.