Réponse :
Explications étape par étape :
A× 4/5 = 8/15
A = 8/15 / (4/5) = 8/15 × 5/4 = (2×4×5)/(3×5×4)= 2/3
B= 2/3 × 5/4 = (2×5)/(3×2×2) = 5/6
5/6 × C = 4/9 ⇒ C = 4/9 /(5/6) = 4/9×6/5=(4×2×3)/(3×3×5)= 8/15
8/15 × D = 4/9 ⇒ D = 4/9/(8/15) = 4/9 × 15/8 = ( 4× 3×5) / (3×3×2×4) = 5/6
5/4 ×E = 5/6 ⇒ E = 5/6 / (5/4) = 5/6 × 4/5 =( 5×2×2) / (2×3×5)= 2/3
donc on a le tableau suivant :
2/3 × 4/5 = 8/15
× × ×
5/4 × 2/3 = 5/6
= = =
5/6 × 8/15 = 4/9
