3 Выполни действия устно наиболее простым способом: a) 3\frac{19}{24} + (5\frac{5}{24} + 1) = б) (16\frac{15}{17} + 4\frac{8}{17}) + (\frac{9}{17} + 2\frac{3}{17}) = в) 7\frac{16}{35} - (3\frac{11}{35} + 4\frac{1}{35}) = г) (4\frac{56}{789} + \frac{15}{789}) - 4\frac{56}{789} = д) (1\frac{6}{39} + 5\frac{16}{39}) - 2\frac{16}{39} = е) 7\frac{13}{14} - (2\frac{1}{14} + 4\frac{17}{14}) =

Выполним вычисления наиболее простым способом:

1. $$3\frac{19}{24} + (5\frac{5}{24} + 1) = (3\frac{19}{24} + 5\frac{5}{24}) + 1 = (3 + 5 + \frac{19}{24} + \frac{5}{24}) + 1 = 8 + \frac{24}{24} + 1 = 8 + 1 + 1 = 10$$
2. $$(16\frac{15}{17} + 4\frac{8}{17}) + (\frac{9}{17} + 2\frac{3}{17}) = (16\frac{15}{17} + 2\frac{3}{17}) + (4\frac{8}{17} + \frac{9}{17}) = (16 + 2 + \frac{15}{17} + \frac{3}{17}) + (4 + \frac{8}{17} + \frac{9}{17}) = 18 + \frac{18}{17} + 4 + \frac{17}{17} = 18 + 1\frac{1}{17} + 4 + 1 = 18 + 1 + 4 + 1 + \frac{1}{17} = 24\frac{1}{17}$$
3. $$7\frac{16}{35} - (3\frac{11}{35} + 4\frac{1}{35}) = 7\frac{16}{35} - 3\frac{11}{35} - 4\frac{1}{35} = 7 - 3 - 4 + \frac{16}{35} - \frac{11}{35} - \frac{1}{35} = 0 + \frac{4}{35} = \frac{4}{35}$$
4. $$(4\frac{56}{789} + \frac{15}{789}) - 4\frac{56}{789} = 4\frac{56}{789} - 4\frac{56}{789} + \frac{15}{789} = 0 + \frac{15}{789} = \frac{15}{789}$$
5. $$(1\frac{6}{39} + 5\frac{16}{39}) - 2\frac{16}{39} = 1\frac{6}{39} + 5\frac{16}{39} - 2\frac{16}{39} = 1\frac{6}{39} + 3 = 4\frac{6}{39} = 4\frac{2}{13}$$
6. $$7\frac{13}{14} - (2\frac{1}{14} + 4\frac{17}{14}) = 7\frac{13}{14} - 2\frac{1}{14} - 4\frac{17}{14} = 7 - 2 - 4 + \frac{13}{14} - \frac{1}{14} - \frac{17}{14} = 1 + \frac{12}{14} - \frac{17}{14} = 1 - \frac{5}{14} = \frac{14}{14} - \frac{5}{14} = \frac{9}{14}$$

Ответ:

1. 10
2. $$24\frac{1}{17}$$
3. $$\frac{4}{35}$$
4. $$\frac{15}{789}$$
5. $$4\frac{2}{13}$$
6. $$\frac{9}{14}$$