5. Вычислите: a) $$(\frac{1}{2}+\frac{3}{17})(5\frac{1}{3}-2\frac{1}{2})$$; б) $$\frac{1}{2}+\frac{3}{17}(5\frac{1}{3}-2\frac{1}{2})$$.

5. Вычислите:

a) $$(\frac{1}{2}+\frac{3}{17})(5\frac{1}{3}-2\frac{1}{2})$$;

$$(\frac{1}{2}+\frac{3}{17})(5\frac{1}{3}-2\frac{1}{2}) = (\frac{1 \cdot 17 + 3 \cdot 2}{2 \cdot 17})(\frac{5 \cdot 3 + 1}{3} - \frac{2 \cdot 2 + 1}{2}) = (\frac{17 + 6}{34})(\frac{16}{3} - \frac{5}{2}) = \frac{23}{34}(\frac{16 \cdot 2 - 5 \cdot 3}{6}) = \frac{23}{34} \cdot \frac{32-15}{6} = \frac{23}{34} \cdot \frac{17}{6} = \frac{23 \cdot 17}{34 \cdot 6} = \frac{23}{2 \cdot 6} = \frac{23}{12} = 1\frac{11}{12}$$

Ответ: $$1\frac{11}{12}$$

б) $$\frac{1}{2}+\frac{3}{17}(5\frac{1}{3}-2\frac{1}{2})$$.

$$\frac{1}{2}+\frac{3}{17}(5\frac{1}{3}-2\frac{1}{2}) = \frac{1}{2}+\frac{3}{17}(\frac{5 \cdot 3 + 1}{3} - \frac{2 \cdot 2 + 1}{2}) = \frac{1}{2} + \frac{3}{17}(\frac{16}{3} - \frac{5}{2}) = \frac{1}{2} + \frac{3}{17} \cdot (\frac{16 \cdot 2 - 5 \cdot 3}{6}) = \frac{1}{2} + \frac{3}{17} \cdot \frac{32-15}{6} = \frac{1}{2} + \frac{3}{17} \cdot \frac{17}{6} = \frac{1}{2} + \frac{3}{6} = \frac{1}{2} + \frac{1}{2} = 1$$

Ответ: 1