Question

Exercițiile 9 și 10

Answer 1

9)

a) 3/2 * 2/9 = 6/18
4/5 + 6/18 = 72/90 + 30/90 = 102/90 = 51/45 = 17/15

b) 2,5 - 0,25 - 2 = 2,25 - 2 = 0,25
0,25*10 = 2,5
2,5 + 1/2 = 5/2 + 1/2 = 6/2 = 3

c) 5,(4) = (54-5)/9 = 49/9
(49/9)^18 : (49/9)^17 = 49/9

d) 1/2 * 21/25 = 21/50
27/25 - 21/50 = 54/50 - 21/50 = 33/50
33/50 * 25/3 (simplificam cu 3) = 11/50 * 25 (simplificam cu 25) = 11/2
11/2 - 1 = 11/2 - 2/2 = 9/2
9/2 * 3013 = 27117 / 2
27117 / 2 - 10^3 = 27117 / 2 - 1000 = 27117 / 2 - 2000/2 = 25117 / 2

e) 65/195 = 1/3 (simpl. cu 65)
108/324 = 1/3 (simpl. cu 108)
122/366 = 1/3 (simpl. cu 122)
1/3 + 1/3 + 1/3 = 3/3 = 1
24/168 = 1/7 (simpl. cu 24)
6/42 = 1/7 (simpl. cu 6)
1/7 - 1/7 = 0/7 = 0
1*0=0

10)

a) a*b + a*c = a*(b+c) = 3/16 * 4/9 = 12/144 = 1/12

b) 9a+4b+5c = 4a+5a+4b+5c = 4a+4b+5a+5c = 4(a+b)+5(a+c) = 4 * 10/3 + 5*5 = 40/3 + 25 = 40/3 + 75/3 = 115/3