5.359 Выполните действие и сократите дробную часть полученного результата: a) 14 5 18' 18 б) 5 6 22 + 22 в) 6-1 12 г) 75 +34.

Решение:

а)

1. $$\frac{14}{18} - \frac{5}{18} = \frac{14-5}{18} = \frac{9}{18}$$
2. $$\frac{9}{18} = \frac{9:9}{18:9} = \frac{1}{2}$$

б)

1. $$\frac{5}{22} + \frac{6}{22} = \frac{5+6}{22} = \frac{11}{22}$$
2. $$\frac{11}{22} = \frac{11:11}{22:11} = \frac{1}{2}$$

в)

1. $$6 - \frac{1}{12} = \frac{6 \cdot 12 - 1}{12} = \frac{72-1}{12} = \frac{71}{12}$$
2. $$\frac{71}{12} = 5\frac{11}{12}$$

г)

1. $$7\frac{5}{27} + 3\frac{4}{27} = 7+3 + \frac{5}{27} + \frac{4}{27} = 10 + \frac{5+4}{27} = 10 + \frac{9}{27} = 10\frac{9}{27}$$
2. $$10\frac{9}{27} = 10\frac{9:9}{27:9} = 10\frac{1}{3}$$

Ответ: а) $$\frac{1}{2}$$; б) $$\frac{1}{2}$$; в) $$5\frac{11}{12}$$; г) $$10\frac{1}{3}$$