1 1/4 times 2 2/3

1. Convert mixed numbers to improper fractions:
1 \frac{1}{4} = \frac{5}{4}
2 \frac{2}{3} = \frac{8}{3}

2. Multiply the improper fractions:
\frac{5}{4} \times \frac{8}{3} = \frac{40}{12}

3. Simplify the resulting fraction:
\frac{40}{12} = \frac{10}{3}

Answer: \frac{10}{3}