8. Completați spațiile libere cu răspunsurile corecte:
a. Dacă x/y = 4/3, y ≠ 0 atunci calculați valoarea raportului 2x+3y/4x+y.
x/y = 3/4 => 4x = 3y => x = 3y/4
2x+3y/4x+y => 2(3y/4)+3y/4(3y/4)+y = 3y/2+3y/4(3y/4)+y = 9y/2/4(3y/4)+y = 9y/2/3y+y = 9y/2/4y = 9/8
b. Dacă x/y = 7/9, y ≠ 0, atunci calculați valoarea raportului x+2y/3x+y.
x/y = 7/9 => 9x = 7y => x = 7y/9
x+2y/3x+y => 7y/9+2y/3(7y/9)+y = 25y/9/3(7y/9)+y = 25y/9/7y/3+y = 25y/9/10y/3 = 5/6
c. Dacă x/2 = y/5, atunci calculați valoarea raportului 7x-2y/x+4y.
x/2 = y/5 => 5x = 2y => x = 2y/5
7x-2y/x+4y => 7(2y/5)-2y/2y/5+4y = 14y/5-2y/2y/5+4y = 4y/5/2y/5+4y = 4y/5/22y/5 = 2/11
d. Dacă x/3 = y/11, atunci calculați valoarea raportului 10x-y/x+y.
x/3 = y/11 => 11x = 3y => x = 3y/11
10x-y/x+y => 10(3y/11)-y/3y/11+y = 30y/11-y/3y/11+y = 19y/11/3y/11+y = 19y/11/14y/11 = 19/14
