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To multiply 1 2/3 by 6 1/2, first convert each mixed number to an improper fraction:
1 2/3 = 5/3
6 1/2 = 13/2
Then, multiply the fractions:
(5/3) * (13/2) = 65/6
So, the answer is 65/6, which can be simplified to the mixed number 10 5/6.