(4/7+2/3):13/3=

To solve the expression \((\frac{4}{7} + \frac{2}{3}) : \frac{13}{3}\), we first need to evaluate the sum \(\frac{4}{7} + \frac{2}{3}\).

1. Find a common denominator for the fractions \(\frac{4}{7}\) and \(\frac{2}{3}\). The least common multiple of 7 and 3 is 21.

2. Convert both fractions: \[ \frac{4}{7} = \frac{4 \times 3}{7 \times 3} = \frac{12}{21} \] \[ \frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21} \]

3. Now add the fractions: \[ \frac{12}{21} + \frac{14}{21} = \frac{12 + 14}{21} = \frac{26}{21} \]

4. Now we need to divide \(\frac{26}{21}\) by \(\frac{13}{3}\). Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{26}{21} \div \frac{13}{3} = \frac{26}{21} \times \frac{3}{13} \]

5. Multiply: \[ = \frac{26 \times 3}{21 \times 13} = \frac{78}{273} \]

6. Now simplify the fraction \(\frac{78}{273}\): Both the numerator and the denominator can be divided by 39: \[ \frac{78 \div 39}{273 \div 39} = \frac{2}{7} \]

Thus, the final result is: \[ \frac{2}{7} \]