Multiply. \[ 3 \frac{1}{2} \times 1 \frac{2}{5} \] Write your answer as a mixed number in simplest form.

To multiply the mixed numbers \(3 \frac{1}{2}\) and \(1 \frac{2}{5}\), first convert them to improper fractions. For \(3 \frac{1}{2}\): - Multiply the whole number (3) by the denominator (2): \(3 \times 2 = 6\). - Add the numerator (1): \(6 + 1 = 7\). - Thus, \(3 \frac{1}{2} = \frac{7}{2}\). For \(1 \frac{2}{5}\): - Multiply the whole number (1) by the denominator (5): \(1 \times 5 = 5\). - Add the numerator (2): \(5 + 2 = 7\). - Thus, \(1 \frac{2}{5} = \frac{7}{5}\). Now, multiply the two improper fractions: \[ \frac{7}{2} \times \frac{7}{5} = \frac{7 \times 7}{2 \times 5} = \frac{49}{10}. \] Next, convert \(\frac{49}{10}\) back to a mixed number: - Divide 49 by 10, which gives 4 with a remainder of 9, so: \[ \frac{49}{10} = 4 \frac{9}{10}. \] The answer is: \[ 4 \frac{9}{10}. \]