Question

2 intregi 1 pe 3 inmultit cu 0,(4) -0,(13)inmultit cu 90 pe 91

Answer 1

2 intregi si1/3 este egal cu7/3
0,(4)=4/9
0,(13)=13/99 reluind exercitiul ⇒7/3·4/9-13/99·90/91=28/27-10/77=(77·28)/(77·27)-   (27·10)/(27·77)=(2156-270)/2079=1886/2079

Answer 2

$\displaystyle 2 \frac{1}{3} \cdot 0,(4)-0,(13) \cdot \frac{90}{91} = \frac{7}{3} \cdot \frac{4}{9} - \frac{13}{99} \cdot \frac{90}{91} = \frac{28}{27} - \frac{1170}{9009} = \\ \\ = \frac{28028-3510}{27027} = \frac{24518}{27027} = \frac{1886}{2079}$