Question

two-thirds of the students in harrys math class and three-fifths of the students in amanis math class are boys. which question about the classes is best modeled with a division expression?

if there are 12 boys, how many students are in harrys class?
if there are 24 students, how many boys are in amanis class?
what fraction of the students in harrys class are girls?
what fraction of the students in amanis class are honors students if the fraction is equal to \\(\frac{5}{4}\\) the fraction of students who are boys?

Explanation:

Analyze the given information

We are given:

• Harry's class: \(\frac{2}{3}\) of the students are boys.
• Amani's class: \(\frac{3}{5}\) of the students are boys.

Model the first option

If there are 12 boys in Harry's class, let \(H\) be the total number of students.

$$ \frac{2}{3} \times H = 12 $$

To find \(H\), we solve:

$$ H = 12 \div \frac{2}{3} $$

This is modeled with a division expression.

Model the second option

If there are 24 students in Amani's class, let \(B\) be the number of boys.

$$ B = 24 \times \frac{3}{5} $$

This is modeled with a multiplication expression.

Model the third option

To find the fraction of girls in Harry's class:

$$ 1 - \frac{2}{3} = \frac{1}{3} $$

This is modeled with a subtraction expression.

Model the fourth option

To find the fraction of honors students in Amani's class:

$$ \frac{5}{4} \times \frac{3}{5} = \frac{3}{4} $$

This is modeled with a multiplication expression.

Answer:

• (A) If there are 12 boys, how many students are in Harry's class? (Correct answer)
• (B) If there are 24 students, how many boys are in Amani's class?
• (C) What fraction of the students in Harry's class are girls?
• (D) What fraction of the students in Amani's class are honors students if the fraction is equal to \(\frac{5}{4}\) the fraction of students who are boys?