Question

Efectuati:
a.$- \frac{3}{41}*20 \frac{1}{2} - \frac{8}{3} *(1- \frac{5}{13} : \frac{2}{13} )$
b.$(- \frac{9}{13} )*[-0,(39)]*(- \frac{20}{21} )$

Answer 1

   
[tex]\displaystyle a) \\ - \frac{3}{41} \times 20 \frac{1}{2} - \frac{8}{3} \times \left(1- \frac{5}{13} : \frac{2}{13} \right)= \\ \\ =-\frac{3}{41} \times \frac{41}{2} - \frac{8}{3} \times \left(1- \frac{5}{13} \times \frac{13}{2} \right)= \\ \\ =-\frac{3}{2} - \frac{8}{3} \times \left(1- \frac{5}{2} \right)= \\ \\ =-\frac{3}{2} - \frac{8}{3} \times \left(\frac{2}{2} - \frac{5}{2} \right)= \\ \\ =-\frac{3}{2} - \frac{8}{3} \times \frac{-3}{2} = [/tex]

[tex]\displaystyle =-\frac{3}{2} - \frac{8}{3} \times \left(-\frac{3}{2}\right) = \\ \\ =-\frac{3}{2} + \frac{8}{3} \times \frac{3}{2} = -\frac{3}{2} + \frac{8}{2} =\boxed{\frac{5}{2}} [/tex]


[tex]\displaystyle b) \\ (- \frac{9}{13} ) \times [-0,(39)] \times (- \frac{20}{21} )= \\ \\ =(- \frac{9}{13} ) \times [-\frac{39}{99}] \times (- \frac{20}{21} )= \\ \\ =- \frac{9}{13} \times \frac{39}{99} \times \frac{20}{21} = \\ \\ =- \frac{1}{1} \times \frac{3}{11} \times \frac{20}{21} =- \frac{1}{1} \times \frac{1}{11} \times \frac{20}{7} = \boxed{- \frac{20}{77} }[/tex]