2/8*8/8+(10/3-13/5):7/15

To evaluate the expression \( \frac{2}{8} \cdot \frac{8}{8} + \left( \frac{10}{3} - \frac{13}{5} \right) : \frac{7}{15} \), we can simplify it step by step. 1. Start by simplifying \( \frac{2}{8} \cdot \frac{8}{8} \): \[ \frac{2}{8} = \frac{1}{4} \] \[ \frac{8}{8} = 1 \] Thus, \[ \frac{2}{8} \cdot \frac{8}{8} = \frac{1}{4} \cdot 1 = \frac{1}{4} \] 2. Next, evaluate \( \frac{10}{3} - \frac{13}{5} \): To subtract these fractions, find a common denominator. The least common multiple of 3 and 5 is 15. Convert each fraction: \[ \frac{10}{3} = \frac{10 \cdot 5}{3 \cdot 5} = \frac{50}{15} \] \[ \frac{13}{5} = \frac{13 \cdot 3}{5 \cdot 3} = \frac{39}{15} \] Now subtract: \[ \frac{10}{3} - \frac{13}{5} = \frac{50}{15} - \frac{39}{15} = \frac{50 - 39}{15} = \frac{11}{15} \] 3. Now evaluate \( \left( \frac{10}{3} - \frac{13}{5} \right) : \frac{7}{15} \): Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{11}{15} : \frac{7}{15} = \frac{11}{15} \cdot \frac{15}{7} = \frac{11 \cdot 15}{15 \cdot 7} = \frac{11}{7} \] 4. Now combine the results: \[ \frac{1}{4} + \frac{11}{7} \] Again, we need a common denominator to add these fractions. The least common multiple of 4 and 7 is 28. Convert each fraction: \[ \frac{1}{4} = \frac{1 \cdot 7}{4 \cdot 7} = \frac{7}{28} \] \[ \frac{11}{7} = \frac{11 \cdot 4}{7 \cdot 4} = \frac{44}{28} \] Now add: \[ \frac{1}{4} + \frac{11}{7} = \frac{7}{28} + \frac{44}{28} = \frac{7 + 44}{28} = \frac{51}{28} \] Thus, the final result is: \[ \frac{51}{28} \]