Question

h) 2,0(1) +2,01(12)-1,2(102)
j)1,1+ 1,(1)-1,1(1)
k)0,(3) · 1,2 ÷ 2,1(6)
l)2,(2)÷2,2 ·2,2(2)
m)1,(5)=1,5- 1,5(1) ÷1,1(5)
REPEDEEE

Answer 1

h)
$2,0(1) +2,01(12)-1,2(102) = \\ = 2\frac{1}{90} + 2\frac{112-1}{9900} -1 \frac{2102-2}{9990} = \\ = \frac{2*90+1}{90} + \frac{2*9900+111}{9900} - \frac{1*9990+2100}{9990} = \\ = \frac{180+1}{90} + \frac{19800+111}{9900} - \frac{9990+2100}{9990} = \\ = \frac{181}{90} + \frac{19911}{9900} - \frac{12090}{9990}$
j)
 $1,1+ 1,(1)-1,1(1)= \\ = 1\frac{11}{10}+ 1\frac{1}{9}- 1 \frac{11-1}{90}=\\= \frac{1*10+11}{10}+ \frac{1*9+1}{9}- \frac{1*90+10}{90}=\\= \frac{10+11}{10}+ \frac{9+1}{9}- \frac{90+10}{90}=\\= \frac{21}{10}+ \frac{10}{9}- \frac{100}{90}=\\= \frac{21*9}{90}+ \frac{10*10}{90}- \frac{100}{90}=\\= \frac{189}{90}+ \frac{100}{90}- \frac{100}{90}=\\= \frac{189}{90} =\\= \frac{21}{10} =\\=2,1$
k)
 $0,(3) * 1,2 : 2,1(6) =\\= \frac{1}{3}* \frac{12}{10} : 2\frac{16-1}{90} =\\= \frac{12}{30} : \frac{2*90+15}{90} =\\=\frac{12}{30} : \frac{180+15}{90} =\\=\frac{12}{30} : \frac{195}{90} =\\= \frac{12}{30} : \frac{65}{30} =\\= \frac{12}{65}$
l)
 $2,(2):2,2 *2,2(2)=\\= 2 \frac{2}{9}: \frac{22}{10}*2 \frac{22-2}{90} =\\= \frac{2*9+2}{9}: \frac{22}{10}* \frac{2*90+20}{90} =\\=\frac{18+2}{9}: \frac{22}{10}* \frac{180+20}{90} =\\= \frac{20}{9}: \frac{22}{10}* \frac{200}{90} =\\= \frac{20}{9}* \frac{10}{22}* \frac{20}{9} =\\= \frac{4000}{1782}$
m)
 $1,(5)-1,5- 1,5(1) :1,1(5) =\\= 1 \frac{5}{9}-\frac{15}{10}-1 \frac{51-5}{90}:1 \frac{15-1}{90}=\\=\frac{1*9+5}{9}-\frac{15}{10}-\frac{1*90+46}{90}:\frac{1*90+14}{90} =\\=\frac{9+5}{9}-\frac{15}{10}-\frac{90+46}{90}:\frac{90+14}{90} =\\=\frac{14}{9}-\frac{15}{10}-\frac{136}{90}:\frac{104}{90} =\\= \frac{140}{90}-\frac{135}{90}-\frac{136}{90}*\frac{90}{104} =\\= \frac{5}{90}-\frac{136}{104} =\\=\frac{1}{18}-\frac{17}{13} =\\= \frac{13-17*18}{234} =\\= \frac{13-306}{234} =\\= \frac{ -293}{234}$