1(1)/(5)times 3(2)/(3)= If the product is a whole number, draw a bench beside the school. If the product is in fifths, draw a hat on the original student.

To solve this problem, we need to multiply the mixed numbers $1\frac {1}{5}$ and $3\frac {2}{3}$.<br /><br />Step 1: Convert the mixed numbers to improper fractions.<br />$1\frac {1}{5} = \frac{6}{5}$<br />$3\frac {2}{3} = \frac{11}{3}$<br /><br />Step 2: Multiply the improper fractions.<br />$\frac{6}{5} \times \frac{11}{3} = \frac{66}{15}$<br /><br />Step 3: Simplify the fraction.<br />$\frac{66}{15} = \frac{44}{10} = 4\frac{4}{10} = 4\frac{2}{5}$<br /><br />Since the product is in fifths, we draw a hat on the original student.<br /><br />Therefore, the answer is $4\frac{2}{5}$.