Question

Determină nr naturale nenule x y, astfel incat fractiile urmatoare sa fie reprezentanti ai aceluiasi nr rational:
a) 3 supra 5,x supra 35,30 supra y
b) 13 supra 14, 65 supra x, y supra 56
c) 85 supra x, 34 supra 26, y supra 78

Va rog, ajutati -ma..!! ❤

Answer 1

$a) \frac{3}{5}= \frac{x}{35} =\frac{30}{y} \\ \\ \frac{3}{5}= \frac{x}{35} \\ \\ x= \frac{3\cdot35}{5}=21 \\ \\ \frac{3}{5} =\frac{30}{y} \\ \\ y= \frac{30\cdot5}{3}=50 \\ \\ x=21; y=50$

$b) \frac{13}{14}= \frac{65}{x} =\frac{y}{56} \\ \\ \frac{13}{14}= \frac{65}{x} \\ \\ x= \frac{14\cdot65}{13} \\ \\ x=70 \\ \\ \frac{13}{14}= \frac{y}{56} \\ \\ y= \frac{13\cdot56}{14} =52 \\ \\ x=70 ; y=52$


$c) \frac{85}{x}= \frac{34}{26}= \frac{y}{78} \\ \\ \frac{85}{x}= \frac{34}{26} \\ \\ x= \frac{85\cdot26}{34}=65 \\ \\ \frac{34}{26}= \frac{y}{78} \\ \\ y= \frac{34\cdot78}{26}=102 \\ \\ x=65;y=102$

Answer 2

a) 3/5; x/35; 30/y, deci:
    3/5 = x/35 și 3/5 = 30/y;
   Acum putem afla : x = 35.3/5 = 21; y = 5.30/3 = 50
b) 13/14 = 65/x = y/56;
    13/14 = 65/x; x = 14.65/13 = 14.5 = 70;
    13/14 = y/56; y = 56.13/14 = 4.13 = 52;
c) 85/x = 34/26 = y/78;
    85/x = 34/26; x = 85.26/34 = 65
    34/26 = y/78; y = 34.78/26 = 102