2.398 Вычислите: a) (4 3/4 - 3 1/12) * 4; б) (5 14/19 - 5 1/38) * 38; в) 7 4/19 * 6 1/4 + 4 15/19 * 6 1/4; г) 3 1/14 * 17 7/29 - 3 1/14 * 3 7/29; e) 2 2/3 * (2 1/16 - 1 7/8).

a) $$\left(4 \frac{3}{4} - 3 \frac{1}{12}\right) \cdot 4 = \left(\frac{4 \cdot 4 + 3}{4} - \frac{3 \cdot 12 + 1}{12}\right) \cdot 4 = \left(\frac{16+3}{4} - \frac{36+1}{12}\right) \cdot 4 = \left(\frac{19}{4} - \frac{37}{12}\right) \cdot 4 = \left(\frac{19 \cdot 3 - 37}{12}\right) \cdot 4 = \frac{57-37}{12} \cdot 4 = \frac{20}{12} \cdot 4 = \frac{20}{3} = 6 \frac{2}{3}$$

Ответ: $$6 \frac{2}{3}$$

б) $$\left(5 \frac{14}{19} - 5 \frac{1}{38}\right) \cdot 38 = \left(\frac{5 \cdot 19 + 14}{19} - \frac{5 \cdot 38 + 1}{38}\right) \cdot 38 = \left(\frac{95 + 14}{19} - \frac{190 + 1}{38}\right) \cdot 38 = \left(\frac{109}{19} - \frac{191}{38}\right) \cdot 38 = \left(\frac{109 \cdot 2 - 191}{38}\right) \cdot 38 = 218 - 191 = 27$$

Ответ: 27

в) $$7 \frac{4}{19} \cdot 6 \frac{1}{4} + 4 \frac{15}{19} \cdot 6 \frac{1}{4} = 6 \frac{1}{4} \cdot \left(7 \frac{4}{19} + 4 \frac{15}{19}\right) = 6 \frac{1}{4} \cdot \left(7 + 4 + \frac{4+15}{19}\right) = 6 \frac{1}{4} \cdot \left(11 + \frac{19}{19}\right) = 6 \frac{1}{4} \cdot (11 + 1) = 6 \frac{1}{4} \cdot 12 = \frac{6 \cdot 4 + 1}{4} \cdot 12 = \frac{24+1}{4} \cdot 12 = \frac{25}{4} \cdot 12 = 25 \cdot 3 = 75$$

Ответ: 75

г) $$3 \frac{1}{14} \cdot 17 \frac{7}{29} - 3 \frac{1}{14} \cdot 3 \frac{7}{29} = 3 \frac{1}{14} \cdot \left(17 \frac{7}{29} - 3 \frac{7}{29}\right) = 3 \frac{1}{14} \cdot \left(17 - 3 + \frac{7-7}{29}\right) = 3 \frac{1}{14} \cdot (14 + 0) = 3 \frac{1}{14} \cdot 14 = \frac{3 \cdot 14 + 1}{14} \cdot 14 = \frac{42+1}{14} \cdot 14 = \frac{43}{14} \cdot 14 = 43$$

Ответ: 43

e) $$2 \frac{2}{3} \cdot \left(2 \frac{1}{16} - 1 \frac{7}{8}\right) = \frac{2 \cdot 3 + 2}{3} \cdot \left(\frac{2 \cdot 16 + 1}{16} - \frac{1 \cdot 8 + 7}{8}\right) = \frac{6+2}{3} \cdot \left(\frac{32+1}{16} - \frac{8+7}{8}\right) = \frac{8}{3} \cdot \left(\frac{33}{16} - \frac{15}{8}\right) = \frac{8}{3} \cdot \left(\frac{33 - 15 \cdot 2}{16}\right) = \frac{8}{3} \cdot \frac{33 - 30}{16} = \frac{8}{3} \cdot \frac{3}{16} = \frac{1}{2}$$

Ответ: $$\frac{1}{2}$$