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what is 3 and 1/2 divided by 5 and 2/3?

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2 Answers

        3½ = 3+1/2 = 7/2  (7 = 2*3+1)  
                 5+2/3 = 17/3 
(7/2) ÷ (17/3) = (7/2) * (3/17) = (7*3)/(2*17) = 21/34
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multiply first fraction by reciprocal  of a second fraction 
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P.S. If we are using slash "/" instead of a fraction bar "—", parentheses are very important to keep right order of operation.

3 1/2 divide 5 2/3  change mixed numerals into improper fractions

7/2 divide 17/3  recipricate the fraction on your right(switch numerator and denominator) then multiply.

7/2*3/17=21/34