Question

1,(3)-0,1(25):0,4 ??????

Answer 1

 

$\displaystyle\bf\\1,\!(3)-0,\!1(25):0,\!4=?\\\\Fiecare~numar~zecimal~il~transformam~in~fractie.\\\\1,\!(3)=\frac{13-1}{9}=\frac{12}{9}\\\\0,\!1(25)=\frac{125-1}{990}=\frac{124}{990}\\\\0,4=\frac{4}{10}\\\\Rezolvare:\\\\1,\!(3)-0,\!1(25):0,\!4=\\\\\frac{12}{9}-\frac{124}{990}:\frac{4}{10}=\\\\\\=\frac{12}{9}-\frac{124}{990}\times\frac{10}{4}=\\\\\\=\frac{12}{9}-\frac{124\times10}{990\times4}=~~~(Simplificam~990~cu~10~si~124~cu~4.)$

.

$\displaystyle\bf\\=\frac{^{11)}12}{~~~9}-\frac{31}{99}=~~~(Amplificam~cu~11~prima~fractie.)\\\\=\frac{132}{99}-\frac{31}{99}=\frac{101}{99}~~~(Transformam~in~numar~zecimal)\\\\\\101:99=1~rest~2\\\\\implies\frac{101}{99}=1\frac{02}{99}=\boxed{\bf1,\!(02)}$