Salut !
Exercice 3 :
Pour simplifier une fraction, il faut trouver le plus grand diviseur commun.
[tex] \frac{-42}{-77}= \frac{-7*6}{-7*11}= \frac{6}{11} \\ \\ \frac{72}{180}= \frac{9*8}{9*20}= \frac{8}{20} = \frac{4*2}{4*5}= \frac{2}{5} \\ \\ \frac{450}{-300}= \frac{150*3}{150*(-2)} = \frac{3}{-2}= -\frac{3}{2} \\ \\ \frac{3*15*(-2)}{18*25}= \frac{3*5*3*(-2))}{3*6*5*5} = \frac{-6}{30} = \frac{-1*6}{6*5}= \frac{-1}{5} [/tex]
Exercice 2 :
Une fraction irréductible est une fraction qui ne peut plus se simplifier.
[tex]A = \frac{-1}{4} + \frac{5}{4} \\ \\ A = \frac{4}{4} \\ \\ A = 1 [/tex]
[tex]B = 3+ \frac{4}{5} \\ \\ B = \frac{3*5}{1*5} + \frac{4}{5} \\ \\ B = \frac{15}{5} + \frac{4}{5} \\ \\ B = \frac{19}{5} [/tex]
[tex]C = \frac{-5}{7}+ \frac{-6}{8} \\ \\ C = \frac{-5*8}{7*8}+ \frac{-6*7}{7*8} \\ \\ C = \frac{-40}{56} + \frac{-42}{56} \\ \\ C = \frac{-82}{56} \\ \\ C = \frac{2*(-41)}{2*28} \\ \\ C = \frac{-41}{28} [/tex]
[tex]D = \frac{5}{12} - \frac{3}{4} \\ \\ D = \frac{5}{12}- \frac{3*3}{4*3} \\ \\ D = \frac{5}{12}- \frac{9}{12} \\ \\ D = \frac{-4}{12} = \frac{4*(-1)}{4*3}= \frac{-1}{3} [/tex]
[tex]E = \frac{-2}{21} + \frac{5}{14} \\ \\ E = \frac{-2*2}{21*2} + \frac{5*3}{14*3} \\ \\ E = \frac{-4}{42}+ \frac{15}{42} \\ \\ E = \frac{11}{42} [/tex]
[tex]F = \frac{1}{15} - \frac{-3}{10} \\ \\ F =\frac{2*1}{15*2} - \frac{-3*3}{10*3} \\ \\ F = \frac{2}{30}- \frac{-9}{30} \\ \\ F = \frac{11}{30} [/tex]
Exercice 3 :
[tex]G = 4* \frac{-3}{28} \\ \\ G = \frac{4*(-3)}{4*7} \\ \\ G = \frac{-3}{7} \\ \\ \\ H = \frac{-2}{5} * \frac{-7}{9} \\ \\ H = \frac{14}{45} [/tex]
[tex]I = \frac{-12}{30} * \frac{25}{-16} \\ \\ I = \frac{-4*3*5*5}{5*6*(-4)*4} \\ \\ I = \frac{15}{24} \\ \\ I = \frac{5*3}{8*3}= \frac{5}{8} \\ \\ \\ J= \frac{7}{-12} * \frac{-3}{15} * \frac{-25}{21} \\ \\ J = \frac{7*(-3)*(-5)*5}{-3*4*5*3*7*3} \\ \\ J = \frac{-5}{36} [/tex]
J'espère t'avoir aidé(e) ! :)
