Question

Transformând mai întâi fracţii zecimale în fracţii ordinare, efectuați:
a) 3,1+3,(1)=
b) 0,02+0,(02)=
c) 2,(3)+1,(2)=
d) 0,(14)+0,41)=
e) 0,(1)+0,(12)+0,(123)=
f) 2,1(2)-1,2(1)=
g) 2,0(1)+2,01(12)-1,2(102)=
h) 2,0(1)+2,01(12)+1,2(102)=
i) 1,1+1,(1)-1,1(1)=
j) 1,2(3)+2,02(03)-3,1(012)=
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)=



VĂ ROOOOG!!!​

Answer 1

Răspuns:

Explicație pas cu pas:

a)

$\frac{31}{10}+\frac{28}{9}=\frac{31*9+28*10}{90}=\frac{279+280}{90}=\frac{559}{90}=6,2(1)$

b)

$\frac{2}{100}+\frac{2}{99}=\frac{2*99+2*100}{9900}=\frac{198+200}{9900}=\frac{398}{9900}=0,04(02)$

c)

$\frac{21}{9}+\frac{11}{9}=\frac{32}{9}=3,(5)$

d) - lipseste o paranteza la 0,41) , asa ca facem mai intai cu 0,4(1) apoi cu 0,(41)

$0,(14)+0,4(1)=\frac{14}{99}+\frac{37}{90}=\frac{14*90+37*99}{8910}=\frac{1260+3663}{8910}=\frac{4923}{8910}=0,5(52)$

si

$0,(14)+0,(41)=\frac{14}{99}+\frac{41}{99}=\frac{55}{99}=0,(5)$

e)

$\frac{1}{9}+\frac{12}{99}+\frac{123}{999}=\frac{1}{9}*(1+\frac{12}{11}+\frac{123}{111})=\frac{1}{9}*\frac{11*111+12*111+123*11}{11*111}=\frac{1221+1332+1353}{10989}=\\\\=\frac{3906}{10989}=0,(355446)$

f)

$\frac{191}{90}-\frac{109}{90}=\frac{191-109}{90}=\frac{82}{90}=0,9(1)$

g)

$\frac{181}{90}+\frac{19911}{9900}-\frac{12090}{9990}=$

$=\frac{1}{90}(181+\frac{19911}{110}-\frac{12090}{111})=$

$=\frac{1}{90}*\frac{181*110*111+19911*111-12090*110}{110*111}=$

$=\frac{2210010+2210121-1329900}{90*110*111}=$

$=\frac{3090231}{1098900}= 2,812(113022)$

h)

$\frac{181}{90}+\frac{19911}{9900}+\frac{12090}{9990}=$

$=\frac{1}{90}(181+\frac{19911}{110}+\frac{12090}{111})=$

$=\frac{1}{90}*\frac{181*110*111+19911*111+12090*110}{110*111}=$

$=\frac{2210010+2210121+1329900}{90*110*111}=$

$=\frac{5750031}{1098900}= 5,232(533442)$