Question

Raportul  dintre a si b este  2/3  si raportul  dintre b si c este 4/9 .
Aflati  raportul dintre:
a) 2a si 3b
b) a+b si 2b 
c) dintre b² si 2c² .

Answer 1

a) a/b = 2/3=> 3a = 2b => a=2b/3
2a/3b = (2* 2b/3) / 3b = 4b/3 * 1/3b = 4b/9b = 4/9
b)a= 2b/3
a+b/2b = (2b/3 + b) / 2b = (2b/3 + 3b/3) /2b = 5b/3 * 1/2b = 5b/6b = 5/6
c) b/c = 4/9 => 4c = 9b = > b = 4c/9
b² /2c² = (4c/9)²/2c² = 16c²/81 * 1/2c² =16c²/81c² = 16/81

Answer 2

Rezolvare a/b=2/3 si b/c=4/9 a) 2a/3b=? a/b=2/3  ⇒   a=2b/3  ⇒ 2a/3b=(4b/3)/3b=(4b/3) ×(1/3b)=4/9. 2a/3b=4/9 b) (a+b)/2b=? a/b=2/3  ⇒   a=2b/3  ⇒ (a+b)/2b=(2b/3+b)/2b=(2b/3+b) ×(1/2b)=(5b/3) ×(1/2b)=5/6 (a+b)/2b=5/6 c) b²/2c²=? b/c=4/9 ⇒ b=4c/9 ⇒ b²/2c²=(4c/9) ² /2c² =(16c²/81)/2c²= =(16c²/81) × (1/2c²)=8/81 b²/2c²=8/81