Let's solve the questions step by step.

Question 1.1: How many learners have blue eyes?

We are given that $\frac{1}{6}$ of the 24 students have blue eyes.

$\text{Number of students with blue eyes} = \frac{1}{6} \times 24 = 4$

So, 4 students have blue eyes.

Question 1.2: How many learners do not have blue or green eyes?

We are given that $\frac{3}{8}$ of the 24 students have green eyes.

$\text{Number of students with green eyes} = \frac{3}{8} \times 24 = 9$

Total students with blue or green eyes:

$4 + 9 = 13$

Students who do not have blue or green eyes:

$24 - 13 = 11$

So, 11 students do not have blue or green eyes.

Question 2: Calculate the breadth of the rectangle

We are given:

• Area = $18 \frac{1}{3}$ cm² = $\frac{55}{3}$ cm² (converted to improper fraction)
• Length = 5 cm

We use the formula:

$\text{Area} = \text{Length} \times \text{Breadth}$

$\frac{55}{3} = 5 \times \text{Breadth}$

Solving for breadth:

$\text{Breadth} = \frac{55}{3} \div 5 = \frac{55}{3} \times \frac{1}{5} = \frac{55}{15} = \frac{11}{3} = 3\frac{2}{3} \text{ cm}$

So, the breadth is $\mathbf{3 \frac{2}{3} \text{ cm}}$.

Would you like a more detailed breakdown? Here are five related questions:

1. If another $\frac{1}{4}$ of the students had brown eyes, how many would that be?
2. What percentage of the students have blue eyes?
3. If the rectangle’s length was doubled, what would the new area be?
4. If 2 more students joined the class and they both had green eyes, how many students would now have green eyes?
5. If a square had the same area as the rectangle, what would its side length be?

Tip: When working with fractions, always convert mixed numbers to improper fractions before performing operations!