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To multiply 1 2/3 by 6 1/2, we can first convert the mixed numbers to improper fractions and then multiply them.
1 2/3 is the same as (3*1 + 2)/3 = 5/3.
6 1/2 is the same as (2*6 + 1)/2 = 13/2.
Now, we can multiply the fractions:
(5/3) * (13/2) = (5 * 13) / (3 * 2) = 65/6.
To convert the answer to a mixed number, we divide the numerator by the denominator:
65 ÷ 6 = 10 remainder 5.
So, the answer is 10 5/6 as a mixed number.