5. produsul mezilor = produsul extremilor
3/2a = b/8 ⇒ 2a×b = 3×8
2ab = 24
ab = 12
6. a) 4/3/x = 6/1/10
4/3×1/10 = 6x
4/30 = 6x
x = 2/15:6
x = 2/15×1/6
x = 1/45
b) 2a divide 6 → a = 4
x/24 = (36-1)/56
x/24 = 35/56
56x = 24×35
x = 840/56
x = 15
7. x+y = 66 ⇒ x = 66-y
x/y = 4/7 ⇒ 7x = 4y
7(66-y) = 4y
462-7y = 4y
-7y -4y = -462
-11y = -462
y = 462/11 ⇒ y = 42
x = 66-42 ⇒ x = 24
8. x/y = 2 ⇒ x = 2y
(x+3y) / (4x+y) = (2y+3y) / (8y+y) = 5y / 9y = 5/9
9. a/b = 10²⁶/5³⁹
10²⁶ = (10²)¹³ = 100¹³
5³⁹ = (5³)¹³ = 125¹³
Am adus la același exponent pentru a compara doar bazele. Dacă 100 < 125 atunci 10²⁶ < 5³⁹ ⇒ a < b
10. (2n-6) / 24 = 10/15
2n-6 = 2/3 × 1/24
2n-6 = 1/36
2n = 1/36 + 6 amplifici 6 cu 36
2n = 217/36
n = 217/36 × 1/2
n = 217/72
11. 0,2(12) = (212-2)/990 = 210/990 = 21/99
1,(27) = (127-1)/99 = 126/99
Raportul lor 0,2(12)/1,(27) = 21/99 : 126/99 = 21/99 × 99/126 = 21/126 = 1/6
13. 1,(03) = (103-1)/99 = 102/99
0,1(21) = (121-1)/990 = 120/990 = 2/99
Raportul lor 1,(03)/0,1(21) = 102/99 : 2/99 = 102/99 × 99/2 = 2/102 = 1/51
