1 54+311

Выполним сложение:

$$5\frac{1}{4} + 3\frac{8}{11} = \frac{5 \cdot 4 + 1}{4} + \frac{3 \cdot 11 + 8}{11} = \frac{20 + 1}{4} + \frac{33 + 8}{11} = \frac{21}{4} + \frac{41}{11} = \frac{21 \cdot 11}{4 \cdot 11} + \frac{41 \cdot 4}{11 \cdot 4} = \frac{231}{44} + \frac{164}{44} = \frac{231 + 164}{44} = \frac{395}{44} = 8 \frac{43}{44}$$

Ответ: $$8 \frac{43}{44}$$