1. Найдите значение выражения: a) 4 12/13 - 3,36 0,8+1,5 б) 12 3/8+8 5/6 B) 7 9/20 -5 17/30

a) Найдем значение выражения:

$$4\frac{12}{13} - 3.36 \div 0.8 + 1.5$$

1) $$4\frac{12}{13} = \frac{4 \cdot 13 + 12}{13} = \frac{52+12}{13} = \frac{64}{13}$$

2) $$3.36 \div 0.8 = 33.6 \div 8 = 4.2$$

3) $$0.8 + 1.5 = 2.3$$

4) $$4.2 \div 2.3 = \frac{42}{10} \div \frac{23}{10} = \frac{42}{10} \cdot \frac{10}{23} = \frac{42}{23} = 1\frac{19}{23}$$

5) $$\frac{64}{13} - 1\frac{19}{23} = \frac{64}{13} - \frac{1 \cdot 23 + 19}{23} = \frac{64}{13} - \frac{42}{23} = \frac{64 \cdot 23 - 42 \cdot 13}{13 \cdot 23} = \frac{1472 - 546}{299} = \frac{926}{299} = 3\frac{29}{299}$$

б) Найдем значение выражения:

$$12\frac{3}{8} + 8\frac{5}{6}$$

1) $$12\frac{3}{8} = \frac{12 \cdot 8 + 3}{8} = \frac{96+3}{8} = \frac{99}{8}$$

2) $$8\frac{5}{6} = \frac{8 \cdot 6 + 5}{6} = \frac{48+5}{6} = \frac{53}{6}$$

3) $$\frac{99}{8} + \frac{53}{6} = \frac{99 \cdot 3 + 53 \cdot 4}{24} = \frac{297 + 212}{24} = \frac{509}{24} = 21\frac{5}{24}$$

в) Найдем значение выражения:

$$7\frac{9}{20} - 5\frac{17}{30}$$

1) $$7\frac{9}{20} = \frac{7 \cdot 20 + 9}{20} = \frac{140+9}{20} = \frac{149}{20}$$

2) $$5\frac{17}{30} = \frac{5 \cdot 30 + 17}{30} = \frac{150+17}{30} = \frac{167}{30}$$

3) $$\frac{149}{20} - \frac{167}{30} = \frac{149 \cdot 3 - 167 \cdot 2}{60} = \frac{447 - 334}{60} = \frac{113}{60} = 1\frac{53}{60}$$

Ответ: a) $$3\frac{29}{299}$$, б) $$21\frac{5}{24}$$, в) $$1\frac{53}{60}$$