To solve \(4 \frac{2}{3} \times 1 \frac{1}{2}\), we first convert the mixed numbers into improper fractions.

1. Convert \(4 \frac{2}{3}\):
   \[
   4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}
   \]

2. Convert \(1 \frac{1}{2}\):
   \[
   1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2}
   \]

Now, multiply the two improper fractions:
\[
\frac{14}{3} \times \frac{3}{2} = \frac{14 \times 3}{3 \times 2} = \frac{42}{6} = 7
\]

So, \(4 \frac{2}{3} \times 1 \frac{1}{2} = 7\).

Would you like more details or have any questions?

Here are five related questions:
1. How do you multiply mixed numbers in general?
2. What is the process of converting improper fractions back to mixed numbers?
3. How would you simplify the result of multiplying two fractions if needed?
4. What is the product of \(3 \frac{3}{4} \times 2 \frac{1}{3}\)?
5. Can you solve \(5 \frac{1}{2} \times 3 \frac{2}{5}\)?

**Tip:** When multiplying fractions, always check if you can simplify before multiplying to make calculations easier!

Learn how to multiply the mixed numbers 4 2/3 and 1 1/2 by converting them into improper fractions and following simple multiplication steps. This solution is perfect for students in Grades 5-7 looking to improve their understanding of fraction multiplication.

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