Домашнее задание Найдите сумму: a) $$38\frac{1}{8}+4\frac{5}{24}$$; б) $$4\frac{19}{75}+6\frac{17}{45}$$; Найдите разность: a) $$1-\frac{4}{17}$$; б) $$5-\frac{7}{13}$$; в) $$47\frac{3}{14}+1\frac{8}{21}$$; г) $$54\frac{3}{4}+18\frac{5}{6}$$; б) $$6-5\frac{6}{11}$$; г) $$4\frac{5}{9}-3$$; д) $$28\frac{5}{9}+13\frac{3}{4}$$; е) $$\frac{4}{7}+2\frac{3}{5}$$; д) $$4\frac{9}{16}-2\frac{2}{14}$$; e) $$11\frac{7}{32}-9\frac{11}{64}$$

Решение:

Найдите сумму:

1. a) $$38\frac{1}{8}+4\frac{5}{24} = 38 + \frac{3}{24} + 4 + \frac{5}{24} = 42 + \frac{8}{24} = 42\frac{1}{3}$$


2. б) $$4\frac{19}{75}+6\frac{17}{45} = 10 + \frac{19 \cdot 3}{225} + \frac{17 \cdot 5}{225} = 10 + \frac{57+85}{225} = 10 + \frac{142}{225} = 10\frac{142}{225}$$


3. в) $$47\frac{3}{14}+1\frac{8}{21} = 48 + \frac{3 \cdot 3}{42} + \frac{8 \cdot 2}{42} = 48 + \frac{9+16}{42} = 48 + \frac{25}{42} = 48\frac{25}{42}$$


4. г) $$54\frac{3}{4}+18\frac{5}{6} = 72 + \frac{3 \cdot 3}{12} + \frac{5 \cdot 2}{12} = 72 + \frac{9+10}{12} = 72 + \frac{19}{12} = 73\frac{7}{12}$$


5. д) $$28\frac{5}{9}+13\frac{3}{4} = 41 + \frac{5 \cdot 4}{36} + \frac{3 \cdot 9}{36} = 41 + \frac{20+27}{36} = 41 + \frac{47}{36} = 42\frac{11}{36}$$


6. е) $$\frac{4}{7}+2\frac{3}{5} = 2 + \frac{4 \cdot 5}{35} + \frac{3 \cdot 7}{35} = 2 + \frac{20+21}{35} = 2 + \frac{41}{35} = 3\frac{6}{35}$$

Найдите разность:

1. a) $$1-\frac{4}{17} = \frac{17}{17} - \frac{4}{17} = \frac{13}{17}$$


2. б) $$5-\frac{7}{13} = 4 + \frac{13}{13} - \frac{7}{13} = 4 + \frac{6}{13} = 4\frac{6}{13}$$


3. в) $$6-5\frac{6}{11} = 5 + \frac{11}{11} - 5 - \frac{6}{11} = \frac{5}{11}$$


4. г) $$4\frac{5}{9}-3 = 1\frac{5}{9}$$


5. д) $$4\frac{9}{16}-2\frac{2}{14} = 4\frac{9}{16}-2\frac{1}{7} = 2 + \frac{9 \cdot 7}{112} - \frac{1 \cdot 16}{112} = 2 + \frac{63-16}{112} = 2\frac{47}{112}$$


6. е) $$11\frac{7}{32}-9\frac{11}{64} = 2 + \frac{7 \cdot 2}{64} - \frac{11}{64} = 2 + \frac{14-11}{64} = 2\frac{3}{64}$$

Ответ:

• Сумма: a) $$42\frac{1}{3}$$, б) $$10\frac{142}{225}$$, в) $$48\frac{25}{42}$$, г) $$73\frac{7}{12}$$, д) $$42\frac{11}{36}$$, е) $$3\frac{6}{35}$$


• Разность: a) $$\frac{13}{17}$$, б) $$4\frac{6}{13}$$, в) $$\frac{5}{11}$$, г) $$1\frac{5}{9}$$, д) $$2\frac{47}{112}$$, е) $$2\frac{3}{64}$$