1.398 Вычислите: а) (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.

Выполним действия:

1. а) $$\left(4 \frac{3}{4} - 3 \frac{1}{12}\right) \cdot 4 = \left(\frac{4 \cdot 4 + 3}{4} - \frac{3 \cdot 12 + 1}{12}\right) \cdot 4 = \left(\frac{16 + 3}{4} - \frac{36 + 1}{12}\right) \cdot 4 = \left(\frac{19}{4} - \frac{37}{12}\right) \cdot 4 = \left(\frac{19 \cdot 3}{4 \cdot 3} - \frac{37}{12}\right) \cdot 4 = \left(\frac{57}{12} - \frac{37}{12}\right) \cdot 4 = \frac{57 - 37}{12} \cdot 4 = \frac{20}{12} \cdot 4 = \frac{20 \cdot 4}{12} = \frac{20 \cdot 1}{3} = \frac{20}{3} = 6 \frac{2}{3} $$
2. б) $$\left(5 \frac{14}{19} - 5 \frac{1}{38}\right) \cdot 38 = \left(\frac{5 \cdot 19 + 14}{19} - \frac{5 \cdot 38 + 1}{38}\right) \cdot 38 = \left(\frac{95 + 14}{19} - \frac{190 + 1}{38}\right) \cdot 38 = \left(\frac{109}{19} - \frac{191}{38}\right) \cdot 38 = \left(\frac{109 \cdot 2}{19 \cdot 2} - \frac{191}{38}\right) \cdot 38 = \left(\frac{218}{38} - \frac{191}{38}\right) \cdot 38 = \frac{218 - 191}{38} \cdot 38 = \frac{27}{38} \cdot 38 = 27 $$
3. в) $$7 \frac{4}{19} \cdot 6 \frac{1}{4} + 4 \frac{15}{19} \cdot 6 \frac{1}{4} = \frac{7 \cdot 19 + 4}{19} \cdot \frac{6 \cdot 4 + 1}{4} + \frac{4 \cdot 19 + 15}{19} \cdot \frac{6 \cdot 4 + 1}{4} = \frac{133 + 4}{19} \cdot \frac{24 + 1}{4} + \frac{76 + 15}{19} \cdot \frac{24 + 1}{4} = \frac{137}{19} \cdot \frac{25}{4} + \frac{91}{19} \cdot \frac{25}{4} = \frac{137 \cdot 25}{19 \cdot 4} + \frac{91 \cdot 25}{19 \cdot 4} = \frac{3425}{76} + \frac{2275}{76} = \frac{3425 + 2275}{76} = \frac{5700}{76} = \frac{1425}{19} = 75$$
4. г) $$3 \frac{1}{14} \cdot 17 \frac{7}{29} - 3 \frac{1}{14} \cdot 3 \frac{7}{29} = \frac{3 \cdot 14 + 1}{14} \cdot \frac{17 \cdot 29 + 7}{29} - \frac{3 \cdot 14 + 1}{14} \cdot \frac{3 \cdot 29 + 7}{29} = \frac{42 + 1}{14} \cdot \frac{493 + 7}{29} - \frac{42 + 1}{14} \cdot \frac{87 + 7}{29} = \frac{43}{14} \cdot \frac{500}{29} - \frac{43}{14} \cdot \frac{94}{29} = \frac{43 \cdot 500}{14 \cdot 29} - \frac{43 \cdot 94}{14 \cdot 29} = \frac{21500}{406} - \frac{4042}{406} = \frac{21500 - 4042}{406} = \frac{17458}{406} = \frac{8729}{203} = 43 $$

Ответ: а) $$6 \frac{2}{3}$$; б) $$27$$; в) $$75$$; г) $$43$$.