Упр.614 ГДЗ Никольский Потапов 8 класс (Алгебра)

1. а) $$4\frac{2}{21}\cdot 10-19\frac{20}{21}$$;
   б) $$24\frac{8}{4}:4-18\frac{5}{41}:3$$;
   в) $$\frac{3}{4}:\frac{5}{6}+2\frac{1}{2}\cdot\frac{2}{5}-1:1\frac{1}{9}$$;
   г) $$7\frac{1}{2}\cdot2\cdot\frac{2}{3}-12\frac{1}{4}:\frac{7}{2}+3\frac{3}{8}+2\frac{3}{4}$$.

а)

$$4\frac{2}{21}\cdot 10-19\frac{20}{21} = \frac{86}{21}\cdot 10-\frac{419}{21} = \frac{860}{21}-\frac{419}{21} = \frac{441}{21} = 21$$

б)

$$24\frac{8}{41}:4-18\frac{5}{41}:3 = \frac{992}{41}\cdot\frac14-\frac{743}{41}\cdot\frac13 = \frac{248}{41}-\frac{743}{41\cdot 3}$$
$$= \frac{248\cdot 3-743}{41\cdot 3} = \frac{744-743}{123} = \frac{1}{123}$$

в)

$$\frac34:\frac56+2\frac12\cdot\frac25-1:\frac19 = \frac34\cdot\frac65+\frac52\cdot\frac25-1\cdot 9$$
$$= \frac{3\cdot 3}{2\cdot 5}+1-9 = \frac{9}{10}+1-\frac{9}{10} = 1$$

г)

$$7\frac12\cdot 2\frac23-12\frac14:\frac72+3\frac38+2\frac34 = \frac{15}{2}\cdot\frac83-\frac{49}{4}:\frac72+3\frac38+2\frac34$$
$$= 5\cdot 4-\frac{49}{4}\cdot\frac27+3\frac38+2\frac34 = 20-\frac72+5\frac98$$
$$= 20-3\frac12+6\frac18 = 16\frac12+6\frac18 = 22\frac58$$

Ответ

а) $$21$$; б) $$\frac{1}{123}$$; в) $$1$$; г) $$22\frac58$$.