Question

1.Simplificati fractia ordinara 180/144 pana devine ireductibila


2.simplificati fractia ordinara 2^75-2^71 supra 2^74+2/72


3.aduceti la același numitor comun fractiile 11/15 si 7/6

dau coroana, 55 puncte
Rapid va rog!

Answer 1

180/144 = 90/72 =45/36=5/4

2^75-2^71 = 2^71( 2^4 -1) =2^71(16-1) =15 x 2^71
2^74+2^72 =2^72(2^2+1) = 5 x 2^72
15 x 2^71 /5 x 2^72 =  ( se simplifica cu 2^71)   =15/5 x 2 =3/2

11/15  si 7/6 
15 = 3x5
6 = 2x3     => numitorul comun este 2x3x5 =30 
11/15 =22/30  
7/6 = 35/30

Answer 2

1)

$\it \dfrac{\ 180^{(9}}{144} = \dfrac{\ 20^{(4}}{16} =\dfrac{5}{4}$

2)

$\it \dfrac{2^{75}-2^{71}}{2^{74}+2^{72}} = \dfrac{2^{71}\cdot2^4-1\cdot2^{71}}{2^{71}\cdot2^3+2^{71}\cdot2} = \dfrac{2^{71}(2^4-1)}{2^{71}(2^3+2)} =\dfrac{\ 15^{(5}}{10} =\dfrac{3}{2}$

3)

$\it \dfrac{^{2)}11}{\ 15};\ \ \dfrac{^{5)}7}{\ 6} \Longrightarrow \dfrac{22}{30}; \ \ \dfrac{35}{30}$