Question

Calculati:
a) 8,(7) - 3,(2)
b) 11,(12) - 4,(23)
c) 9,2(5) - 6,1(3)
d) 7,(8) - 3,4(5)
e) 12 intregi si 3/4 - 7,2 - 0,(2)

Answer 1

$a). 8,(7)= \frac{87-8}{9} = \frac{79}{9} \\ 3,(2)= \frac{32-3}{9} = \frac{29}{9} \\ 8,(7)-3,(2)= \frac{79}{9} - \frac{29}{9} = \frac{50}{9} \\ b).11,(12)= \frac{1112-11}{99} = \frac{1101}{99} \\ 4,(23)= \frac{423-4}{99} = \frac{419}{99} \\ 11,(12)-4,(23)= \frac{1101}{99} - \frac{419}{99} = \frac{682}{99}$
$c).9,2(5)= \frac{925-92}{90} = \frac{833}{90} \\ 6,1(3)= \frac{613-61}{90} = \frac{552}{90} \\ 9,2(5)-6,1(3)= \frac{883}{90} - \frac{552}{90} = \frac{331}{90} \\ d).7,(8)= \frac{78-7}{9} = \frac{71}{9} \\ 3,4(5)= \frac{345-34}{90} = \frac{311}{90} \\ 7,(8)-3,4(5)= \frac{71}{9} - \frac{311}{90} = \frac{710}{90} - \frac{311}{90} = \frac{399}{90}$
$e).12 \frac{3}{4} = \frac{12*4+3}{4} = \frac{48+3}{4} = \frac{51}{4} \\ 7,2= \frac{72}{10} = \frac{36}{5} \\ 0,(2)= \frac{2}{9} \\ 12 \frac{3}{4} -7,2-0,(2)= \frac{51}{4} - \frac{36}{5} - \frac{2}{9} = \frac{255}{20} - \frac{144}{20} - \frac{2}{9} = \frac{111}{20} - \frac{2}{9} = \\ = \frac{999}{180} - \frac{40}{180} = \frac{959}{180}$