Durée : 45 minutes. Barème sur 20.
Exercice 1 (8 pts)
Calculer et simplifier :
- \(\frac{-9}{14}\times\frac{7}{-12}\) (2 pts)
- \(\frac{5}{8}\div\frac{-15}{4}\) (2 pts)
- \(\frac{-2}{3}\times\frac{9}{4}\times\frac{-1}{6}\) (2 pts)
- \(\frac{\frac{4}{5}}{-2}\) (2 pts)
Correction
- \(\frac{63}{168} = \frac38\). 2. \(\frac58\times\frac{4}{-15} = -\frac16\). 3. \(\frac{18}{72} = \frac14\). 4. \(-\frac25\).
Exercice 2 (8 pts)
On pose \(A = \frac{3}{4} - \frac{1}{2}\times\frac{5}{3}\) et \(B = \left(\frac{3}{4} - \frac{1}{2}\right)\times\frac{5}{3}\).
- Calculer \(A\) et \(B\). (6 pts)
- Calculer \(\frac{A}{B}\). (2 pts)
Correction
- \(A = \frac34 - \frac56 = \frac{9 - 10}{12} = -\frac{1}{12}\). \(B = \frac14\times\frac53 = \frac{5}{12}\).
- \(\frac{A}{B} = -\frac{1}{12}\times\frac{12}{5} = -\frac15\).
Exercice 3 (4 pts)
Un champ de \(\frac{3}{4}\) d'hectare est partagé en \(6\) parcelles égales. Quelle est l'aire d'une parcelle ?
Correction
\(\frac34\div6 = \frac{3}{24} = \frac18\) d'hectare.