Вариант 4. 1. Найдите значение выражения. а). 67/12+ (5³/40 - 4⁸/₁₅); 6). 5²/₃: ¹/₃- 1⁷/₁₂ * 6.

Решение:

а) $$6\frac{7}{12}+ (5\frac{3}{40} - 4\frac{8}{15})$$

1) $$5\frac{3}{40} - 4\frac{8}{15} = \frac{203}{40} - \frac{68}{15} = \frac{203 \cdot 3 - 68 \cdot 8}{120} = \frac{609 - 544}{120} = \frac{65}{120} = \frac{13}{24}$$

2) $$6\frac{7}{12} + \frac{13}{24} = \frac{79}{12} + \frac{13}{24} = \frac{79 \cdot 2 + 13}{24} = \frac{158 + 13}{24} = \frac{171}{24} = \frac{57}{8} = 7\frac{1}{8}$$

б) $$5\frac{2}{3} : \frac{1}{3} - 1\frac{7}{12} \cdot 6$$

1) $$5\frac{2}{3} : \frac{1}{3} = \frac{17}{3} : \frac{1}{3} = \frac{17}{3} \cdot \frac{3}{1} = 17$$

2) $$1\frac{7}{12} \cdot 6 = \frac{19}{12} \cdot 6 = \frac{19 \cdot 6}{12} = \frac{19}{2} = 9\frac{1}{2}$$

3) $$17 - 9\frac{1}{2} = 16\frac{2}{2} - 9\frac{1}{2} = 7\frac{1}{2}$$

Ответ: а) $$7\frac{1}{8}$$; б) $$7\frac{1}{2}$$