Bonjour,
En utilisant la décomposition en produit de facteurs premiers, rendre les fractions suivantes irréductibles en justifiant.
a. 385/ 165
385 = 5 x 7 x 11
165 = 3 x 5 x 11
385/165 = [(5 x 11) x 7] / [(5 x 11) x 3] = (55 x 7) / (55 x 3) = 7/3
b. 153/189
153 = 3 x 3 x 17
189 = 3 x 3 x 3 x 7
153/189 = [(3 x 3) x 17] x [(3 x 3) x (3 x 7)] = (9 x 17) / (9 x 21) = 17/21
c. 120/90
120 = 2 x 2 x 2 x 3 x 5
90 = 2 x 3 x 3 x 5
120/90 = [(2 x 3 x 5) x (2 x 2)] / [(2 x 3 x 5) x 3] = (30 x 4) / (30 x 3) = 4/3
d. 184/316
184 = 2 x 2 x 2 x 23
316 = 2 x 2 x 79
184/316 = [(2 x 2) x (2 x 23)] / [(2 x 2) x 79] = (4 x 46) / (4 x 79) = 46/79
e. 510/195
510 = 2 x 3 x 5 x 17
195 = 3 x 5 x 13
510/195 = [(3 x 5) x (2 x 17)] / [(3 x 5) x 13] = (15 x 34) / (15 x 13) = 34/13
f. 84/300
84 = 2 x 2 x 3 x 7
300 = 2 x 2 x 3 x 5 x 5
84/300 = [(2 x 2 x 3) x 7] / [(2 x 2 x 3) x (5 x 5)] = (24 x 7) / (24 x 25) = 7/25.
