Exercice 4
Opérations avec des fractions; calculer et simplifier en fraction irréductible.
Partie : 1. Multiplication de fractions
Question
Question
b.
\(\cfrac {-15}{16} × \cfrac {17}{-16}\)
Solution
b.
\(\cfrac {-15}{16} × \cfrac {17}{-16}= \cfrac {15 × 17}{16 ×16} = \cfrac {255}{256} \)
Question
c.
\(\cfrac {12}{-37} × \cfrac {37}{13} \)
Solution
c.
\(\cfrac {12}{-37} × \cfrac {37}{13} = -\cfrac {12}{13} \)\(\)
Question
d.
\(\cfrac {-19}{-26} × \cfrac {15}{-38}\)
Solution
d.
\(\cfrac {-19}{-26} × \cfrac {15}{-38}= -\cfrac {19 × 15}{26 ×38} = \cfrac {-19 × 15}{26 × 19 × 2} =\cfrac {-15}{52} \)
Partie : 2. Division de fractions
Question
a.
\(\cfrac{-\cfrac {5}{6} }{\cfrac {-11}{9}}\)
Solution
a.
\(\cfrac{-\cfrac {5}{6} }{\cfrac {-11}{9}} = \cfrac {5}{6} × \cfrac {9}{11} = \cfrac {5×3×3}{2×3×11} = \cfrac {15}{22} \)
Question
b.
\(\cfrac{-\cfrac {1}{-12} }{\cfrac {-7}{36}}\)
Solution
b.
\(\cfrac{-\cfrac {1}{-12} }{\cfrac {-7}{36}} = \cfrac {1}{12} × \cfrac {-36}{7} = \cfrac {-3×12}{12×7} = -\cfrac {3}{7} \)
Question
c.
\(\cfrac{\cfrac {15}{6} }{\cfrac {18}{25}} \)
Solution
c.
\(\cfrac{\cfrac {15}{6} }{\cfrac {18}{25}} = \cfrac {15}{6} × \cfrac {25}{18} = \cfrac {5×3×25}{2×3×18} = \cfrac {125}{36} \)\(\)
Question
d.
\(\cfrac{\cfrac {-14}{17} }{\cfrac {11}{-19}} \)
Solution
d.
\(\cfrac{\cfrac {-14}{17} }{\cfrac {11}{-19}} = \cfrac {14}{17} × \cfrac {19}{11} = \cfrac {266}{187}\)
Partie : 3. Addition de fractions
Question
a.
\(\cfrac {-5}{9} + \cfrac {11}{9}\)
Solution
a.
\(\cfrac {-5}{6} + \cfrac {11}{9}= \cfrac {6}{9} = \cfrac {2}{3}\)
Question
b.
\(\cfrac {5}{-16} + \cfrac {-21}{8}\)
Solution
b.
\(\cfrac {5}{-16} + \cfrac {-21}{8} = \cfrac {-5 - 21 × 2}{16} = \cfrac {-47}{16} \)
Question
c.
\(\cfrac {12}{37} + \cfrac {-37}{13}\)
Solution
c.
\(\cfrac {12}{37} + \cfrac {-37}{13}= \cfrac {12 ×13 - 37 × 37}{37 × 13} = \cfrac {-1213}{481} \)
Partie : 4. Priorités des opérations multiples
Question
a.
\(7 × \left(\cfrac {-5}{9} + \cfrac {11}{9}\right)\)
Solution
a.
\(7 × \left(\cfrac {-5}{9} + \cfrac {11}{9}\right) = 7 × \cfrac {6}{9} = \cfrac {42}{9} \)
Question
b.
\(\cfrac {-2}{3} × \left(\cfrac {-5}{11} + \cfrac {21}{-5}\right) \)
Solution
b.
\(\cfrac {-2}{3} × \left(\cfrac {-5}{11} + \cfrac {21}{-5}\right) = \cfrac {-5 ×(-2)}{11} + \cfrac {2 × 21}{5}= \cfrac {5 × 10 + 11 ×42 }{55} = \cfrac {512}{55} \)
Question
c.
\(\cfrac {12}{37} - \cfrac {2}{3} × \left(\cfrac {12}{13} - \cfrac {1}{7}\right) \)
Solution
c.
\(\cfrac {12}{37} - \cfrac {2}{3} × \left(\cfrac {12}{13} - \cfrac {1}{7}\right) = \cfrac {12}{37} - \cfrac {2 × 12}{3 × 13} + \cfrac {2}{3×7} = -\cfrac {1978}{10101} \)