Bonjour
Utilise les décompositions en produit de
facteurs premiers ci-dessous pour rendre les
fractions irréductibles.
180 = 2^2 x 3^2 x 5
328 = 2^3 x 41
1 449 = 3^2 x 7 x 23
1625 = 5^3 x 13
2009 = 7^2 x 41
3 887 = 13^2 x 23
a. 180/328 = (2^2 x 3^2 x 5)/(2^3 x 41)
180/328 = (3^2 x 5)/(2^(3-2) x 41)
180/328 = 45/(2 x 41)
180/328 = 45/82
b. 1 449/2009 = (3^2 x 7 x 23)/(7^2 x 41)
1449/2009 = (3^2 x 23)/(7^(2-1) x 41)
1449/2009 = (9 x 23)/(7 x 41)
1449/2009 = 207/287
c. 3 887/1449 = (13^2 x 23)/(3^2 x 7 x 23)
= 169/(9 x 7 x 23^(1-1))
= 169/63
d. 1625/3 887 = (5^3 x 13)/(13^2 x 23)
= 5^3/(13^(2-1) x 23)
= 125/(13 x 23)
= 125/299
e. 328/2009 = (2^3 x 41)/(7^2 x 41)
= 2^3/7^2
= 8/49
f. 180/1 625 = (2^2 x 3^2 x 5)/(5^3 x 13)
= (4 x 9)/(5^(3-1) x 13)
= 36/(5^2 x 13)
= 36/(25 x 13)
= 36/325
