3 1/4 x 1 4/9

To multiply the mixed numbers \( 3 \frac{1}{4} \) and \( 1 \frac{4}{9} \), we first convert them to improper fractions.

1. Convert \( 3 \frac{1}{4} \): \[ 3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \]

2. Convert \( 1 \frac{4}{9} \): \[ 1 \frac{4}{9} = \frac{1 \times 9 + 4}{9} = \frac{9 + 4}{9} = \frac{13}{9} \]

Now we multiply the two improper fractions:

\[ \frac{13}{4} \times \frac{13}{9} = \frac{13 \times 13}{4 \times 9} = \frac{169}{36} \]

Next, we can convert this back to a mixed number.

To do this, we divide \( 169 \) by \( 36 \):

• \( 169 \div 36 = 4 \) (since \( 4 \times 36 = 144 \))
• Remainder: \( 169 - 144 = 25 \)

Thus, in mixed number form:

\[ \frac{169}{36} = 4 \frac{25}{36} \]

So, the final answer is:

\[ 3 \frac{1}{4} \times 1 \frac{4}{9} = 4 \frac{25}{36} \]