In a fifth grade class, 2/5 of the students have brown hair. Of the brown-haired students, 1/4 of them have long hair. Of the students with long brown hair, 1/3 of them have green eyes. What fraction of the students in the class have long brown hair?

To find the fraction of students in the class with long brown hair, we'll follow these steps:

1. Find the fraction of students with brown hair.
2. Find the fraction of brown-haired students with long hair.
3. Find the fraction of students with long brown hair.

Given:
- $ \frac{2}{5} $ of the students have brown hair.
- $ \frac{1}{4} $ of brown-haired students have long hair.
- $ \frac{1}{3} $ of long brown-haired students have green eyes.

1. Fraction of students with brown hair: $ \frac{2}{5} $

2. Fraction of brown-haired students with long hair:
$ \frac{2}{5} \times \frac{1}{4} = \frac{2}{20} = \frac{1}{10} $

3. Fraction of students with long brown hair:
$ \frac{1}{10} $

So, 1/10 of the students in the class have long brown hair.

Heather Heather · Answer 2 · 2024-02-21T23:25:29+01:00

Answer: One-tenth of the class has long brown hair.

Step-by-step explanation:

To answer this question, remember that "of" means multiplication in mathematics. Since 2/5 of 1/4 have long brown hair, we can multiply these fractions together. Multiply straight across the numerator and denominator, then simplify the fraction.

[tex]\displaystyle \frac{2}{5} *\frac{1}{4} =\frac{2*1}{5*4} =\frac{2}{20} =\frac{1}{10}[/tex]