Question

a soma de 2, 7666 ... + 1, 44... é igual a :

Answer 1

$2,7666... = 2,7 + 0,0666...\\2,7666... = 2,7 + (0,666.../10)\\2,7666... = 2,7 + ([6/9]/10)\\2,7666... = 2,7 + ([2/3]/10)\\2,7666... = 2,7 + (2/[3*10])\\2,7666... = 2,7 + ([2/3]/10)\\2,7666... = 2,7+(2/30)\\2,7666... = (30*2,7+2)/30\\2,7666... = (81+2)/30\\2,7666... = 83/30$
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$1,444... = 1 + 0,444...\\1,444...=1 + (4/9)\\1,444...=(9*1 + 4) / 9\\1,444...=(9 + 4) / 9\\1,444...=13 / 9$
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$2,7666... + 1,444... = (83/30)+(13/9)\\2,7666... + 1,444... = (3*83/[3*30])+(10*13/[10*9])\\2,7666...+1,444...=(249/90)+(130/90)\\2,7666...+1,444...=(249+130)/90\\2,7666...+1,444...=379/90$