Exercice 1
Simplifier : \(\frac{-12}{18}\) ; \(\frac{21}{-35}\) ; \(\frac{-40}{-56}\).
Correction
\(\frac{-2}{3}\) ; \(-\frac35\) ; \(\frac57\).
Exercice 2
Comparer : \(\frac{-5}{7}\) et \(\frac{-4}{7}\) ; \(\frac{-3}{5}\) et \(\frac{-5}{8}\) ; \(\frac{2}{-9}\) et \(\frac{-1}{3}\).
Correction
\(\frac{-5}{7} < \frac{-4}{7}\). \(\frac{-24}{40} > \frac{-25}{40}\). \(\frac{-2}{9} > \frac{-3}{9}\).
Exercice 3
Calculer : \(A = \frac{3}{8} - \frac{7}{8}\) ; \(B = \frac{-2}{3} + \frac{5}{6}\) ; \(C = \frac{1}{4} - \frac{5}{6}\) ; \(D = -2 + \frac{7}{3}\).
Correction
\(A = -\frac48 = -\frac12\). \(B = \frac{-4 + 5}{6} = \frac16\). \(C = \frac{3 - 10}{12} = -\frac{7}{12}\). \(D = \frac{-6 + 7}{3} = \frac13\).
Exercice 4
Calculer : \(E = \frac12 - \left(\frac{-1}{3}\right) + \left(-\frac{5}{6}\right)\).
Correction
\(E = \frac36 + \frac26 - \frac56 = 0\).
Exercice 5
Un réservoir est rempli aux \(\frac{3}{4}\). On utilise \(\frac{2}{5}\) de sa capacité puis on ajoute \(\frac{1}{10}\). À quelle fraction est-il rempli ?
Correction
\(\frac34 - \frac25 + \frac{1}{10} = \frac{15 - 8 + 2}{20} = \frac{9}{20}\).