Question

Aratati ca media aritmetica a numerelor rationale a=(3/4-1/2) / 1/12 si b =3x(2/3-1/2+1/6) este egala cu 2.

Answer 1

Răspuns:

a = (3/4  -  1/2) / 1/12  = (3/4  -  2/4) :  1/12 =  1/4  :  1/12 =  1/4  x 12/1  = 12/4 = 3

b = 3 x (2/3  -  1/2  +  1/6) = 3 x (4/6  -  3/6  +  1/6) =  3  x  (4-3+1)/6 = 3 x  2/6 = 6/6 = 1

m.a. = (a + b) : 2 = (3 + 1) : 2 = 4 : 2 = 2

Answer 2

$a = \left(\dfrac{3}{4}-\dfrac{1}{2}\right):\dfrac{1}{12} = \left(\dfrac{3}{4}-\dfrac{1}{2}\right)\cdot 12 = 3\cdot 3-6 = 9-6 = 3$

$b = 3\cdot \left(\dfrac{2}{3}-\dfrac{1}{2}+\dfrac{1}{6}\right) = 2-\dfrac{3}{2}+\dfrac{1}{2} =2-\dfrac{2}{2} = 2-1 = 1$

$\Rightarrow m_a = \dfrac{a+b}{2}=\dfrac{3+1}{2} = \dfrac{4}{2} = 2$