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To add these mixed numbers, we need to first convert the mixed numbers to improper fractions.
4 1/3 is equal to (4 * 3 + 1)/3 = 13/3.
3 1/2 is equal to (3 * 2 + 1)/2 = 7/2.
Now, we can add the two improper fractions:
13/3 + 7/2 = (13 * 2 + 7 * 3)/(3 * 2) = 26/3 + 21/3 = 47/3.
The sum in simplest form is 47/3.