The question states:

• $\frac{2}{3}$ of all homeowners have a pet.
• Of those, $\frac{3}{4}$ have either a dog or a cat.

We need to find the fraction of the homeowners who have either a dog or a cat.

Solution:

To solve this, we need to multiply the two fractions:

$\text{Fraction of homeowners with either a dog or cat} = \frac{2}{3} \times \frac{3}{4}$

Multiply the numerators and the denominators:

$\frac{2 \times 3}{3 \times 4} = \frac{6}{12} = \frac{1}{2}$

So, half of the homeowners have either a dog or a cat.

Would you like more details, or do you have any other questions?

Here are 5 related questions:

1. If $\frac{1}{2}$ of all homeowners have either a dog or cat, what fraction have neither?
2. What fraction of the homeowners have pets other than dogs or cats?
3. If 600 homeowners were surveyed, how many have either a dog or cat?
4. If the total number of homeowners is 1,200, how many own pets?
5. If $\frac{3}{4}$ of those with pets have a dog, what fraction of the total homeowners own dogs?

Tip: When multiplying fractions, remember to multiply the numerators and denominators directly, and then simplify if possible.