Bonjour
6/5 + 2/13 ... 9/8 + 3/13
6/5 = (6 x 8)/(5 x 8) = 48/40
9/8 = (9 x 5)/(8 x 5) = 45/40
= (48 x 13)/(40 x 13) + (2 x 40)/(13 x 40)
= 624/520 + 80/520
= 704/520
= (45 x 13)/(40 x 13) + (3 x 40)/(13 x 40)
= 585/520 + 120/520
= 705/520
704/520 < 705/520
Donc : 6/5 + 2/13 < 9/8 + 3/13
(-13/11) - 5/9 ... (-6/5) - 5/9
-13/11 = (-13 x 5)/(11 x 5) = -65/55
-6/5 = (-6 x 11)/(5 x 11) = -66/55
-65/55 > -66/55
Donc (-13/11) - 5/9 > (-6/5) - 5/9
-19/12 + 4,5 ... -14/6 + 3,5
4,5 = (4,5 x 12)/12 = 54/12
3,5 = (3,5 x 12)/12 = 42/12
-14/6 = (-14 x 2)/(6 x 2) = -28/12
-19/12 + 54/12 = 35/12
-28/12 + 42/12 = 14/12
35/12 > 14/12
Donc : -19/12 + 4,5 > -14/6 + 3,5
(-14,6) + 4/7 ... (-14,3) + 9/7
-14,6 = (-14,6 x 7)/7 = -102,2/7
-14,3 = (-14,3 x 7)/7 = -100,1/7
-102,2/7 + 4/7 = -98,2/7
-100,1/7 + 9/7 = -91,1/7
-98,2/7 < -91,1/7
Donc : (-14,6) + 4/7 < (-14,3) + 9/7
