Question

Решите
3,(45):1,(74)=2,(3):х
1,(6):0,8(3)=х:0,(45)
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Answer 1

Пошаговое объяснение:

1.

$3,(45):1,(74)=2,(3):x\\3\frac{45}{99} :1\frac{74}{99}=2\frac{3}{9} :x\\3\frac{5}{11}:\frac{173}{99} =2\frac{1}{3}:x\\\frac{38}{11} :\frac{173}{99} =\frac{7}{3}:x\\\frac{7}{3}: x=\frac{38*99}{11*173}=\frac{38*9}{173}=\frac{342}{173} \\x=\frac{7*173}{3*342}=\frac{1211}{1026} .$

Проверка:

$\frac{38}{11}:\frac{173}{99} =\frac{7}{3}:\frac{1211}{1026} \\\frac{38*99}{11*173}=\frac{7*1026}{3*1211}\\\frac{342}{173}=\frac{342}{173} .$

2.

$1,(6):0,8(3)=x:0,(45)\\1\frac{6}{9}:\frac{83-8}{90}=x:\frac{45}{99} \\1\frac{2}{3}:\frac{75}{90} =x:\frac{5}{11} \\\frac{5}{3}: \frac{5}{6} =x:\frac{5}{11} \\x=\frac{5*6*5}{3*5*11} \\x=\frac{10}{11} .$

Проверка:

$\frac{5}{3} :\frac{5}{6}=\frac{10}{11}:\frac{5}{11} \\\frac{5*6}{3*5}=\frac{10*11}{11*5}\\2=2.$