Упр.614 ГДЗ Никольский Потапов 8 класс (Алгебра)

б) 24*8/4 : 4 — 18*5/41 :3;
в) 3/4:5/6+2*1/2*2/5-1:1*1/9;
г) 7*1/2*2*2/3-12*1/4:7/2+3*3/8+2*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) $$22\frac58$$.