2 4/13 •(4/5-7/12)-7:3 1/2

First, let's simplify the expression step by step:

1. Convert the mixed numbers to improper fractions: \(2 \frac{4}{13} = \frac{2 \times 13 + 4}{13} = \frac{26 + 4}{13} = \frac{30}{13}\) \(\frac{4}{5} = \frac{4}{5}\) \(\frac{7}{12} = \frac{7}{12}\) \(7 \div 3\frac{1}{2} = 7 \div \frac{7 \times 2 + 1}{2} = 7 \div \frac{15}{2} = 7 \times \frac{2}{15} = \frac{14}{15}\)

2. Perform the subtraction inside the parentheses: \(\frac{4}{5} - \frac{7}{12} = \frac{4 \times 12 - 7 \times 5}{5 \times 12} = \frac{48 - 35}{60} = \frac{13}{60}\)

3. Now, substitute the simplified values back into the original expression: \(\frac{30}{13} \times \frac{13}{60} - \frac{14}{15}\)

4. Perform the multiplication: \(\frac{30 \times 13}{13 \times 60} - \frac{14}{15} = \frac{390}{780} - \frac{14}{15}\)

5. Find a common denominator and combine the fractions: \(\frac{390}{780} - \frac{14}{15} = \frac{390 \times 15}{780 \times 15} - \frac{14 \times 52}{15 \times 52}\) \(= \frac{5850}{11700} - \frac{728}{1170}\)

6. Subtract the fractions: \(\frac{5850}{11700} - \frac{728}{1170} = \frac{5850 \times 1170 - 728 \times 780}{11700 \times 1170}\) \(= \frac{6835500 - 567840}{13689000}\) \(= \frac{6267660}{13689000}\)

Therefore, the simplified result of the expression \(2 \frac{4}{13} \times (\frac{4}{5} - \frac{7}{12}) - 7 \div 3 \frac{1}{2}\) is \(\frac{6267660}{13689000}\).