7 13_15-(2 7_15+3 4_15

To solve the expression \( 7 \frac{13}{15} - (2 \frac{7}{15} + 3 \frac{4}{15}) \), we'll follow these steps:

1. Convert mixed numbers to improper fractions.

   • For \( 7 \frac{13}{15} \): \[ 7 \frac{13}{15} = \frac{7 \times 15 + 13}{15} = \frac{105 + 13}{15} = \frac{118}{15} \]
   • For \( 2 \frac{7}{15} \): \[ 2 \frac{7}{15} = \frac{2 \times 15 + 7}{15} = \frac{30 + 7}{15} = \frac{37}{15} \]
   • For \( 3 \frac{4}{15} \): \[ 3 \frac{4}{15} = \frac{3 \times 15 + 4}{15} = \frac{45 + 4}{15} = \frac{49}{15} \]

2. Calculate \( 2 \frac{7}{15} + 3 \frac{4}{15} \): Now we can find: \[ 2 \frac{7}{15} + 3 \frac{4}{15} = \frac{37}{15} + \frac{49}{15} = \frac{37 + 49}{15} = \frac{86}{15} \]

3. Now evaluate \( 7 \frac{13}{15} - (2 \frac{7}{15} + 3 \frac{4}{15}) \): This becomes: \[ 7 \frac{13}{15} - (2 \frac{7}{15} + 3 \frac{4}{15}) = \frac{118}{15} - \frac{86}{15} = \frac{118 - 86}{15} = \frac{32}{15} \]

4. Convert back to a mixed number if needed: \[ \frac{32}{15} = 2 \frac{2}{15} \]

Thus, the final result is: \[ \boxed{2 \frac{2}{15}} \]