Exercice 1 [S'exercer sur les fractions]

Exercice 1

Partie : 1. Égalité de fractions : trouver la valeur de l'entier n tel que :

Question

\(\cfrac {n}{5}=\cfrac {6}{10}\)

Solution

a.

\(n=3\)

Question

\(\cfrac {-2}{11}=\cfrac {n}{33}\)

Solution

b.

\(n=-6\)

Question

\(\cfrac {1}{2}=\cfrac {-3}{n}\)

Solution

c.

\(n=-6\)

Question

\(\cfrac {48}{72}=\cfrac {4}{n}\)

Solution

d.

\(n=-6\)

Partie : 2. Simplifier des fractions : proposer une seconde écriture de la fraction à l'aide de termes plus petits.

Question

\(\cfrac {10}{65} \)

Solution

a.

\(\cfrac {10}{65}=\cfrac {2}{13}\)

Question

\(\cfrac {32}{84}\)

Solution

b.

\(\cfrac {32}{84}=\cfrac {16}{42}=\cfrac {8}{21}\)

Question

\(\cfrac {70}{240}\)

Solution

c.

\(\cfrac {70}{240}=\cfrac {7}{24}\)

Question

\(\cfrac {18}{51}\)

Solution

d.

\(\cfrac {18}{51}=\cfrac {6}{17}\)

Partie : 3. Fractions irréductibles : donner la forme irréductible de chaque fraction.

Question

\(\cfrac {20}{36}=\)

Solution

a.

\(\cfrac {20}{36}=\cfrac {5}{9}\)

Question

\(\cfrac {8}{28}=\)

Solution

b.

\(\cfrac {8}{28}= \cfrac {2}{7}\)

Question

\(\cfrac {120}{35}=\)

Solution

c.

\(\cfrac {120}{35}=\cfrac {24}{7}\)

Question

\(\cfrac{48}{172}\)

Solution

d.

\(\cfrac{48}{172}=\cfrac{12}{43}\)

Partie : 4. Fractions décimales : les nombres désignés par les fractions suivantes sont-ils décimaux ?

Question

\(\cfrac {-12}{6}\)

Solution

a.

La réponse est "oui" :

\(\cfrac {-12}{6}=-2\)

Question

\(\cfrac {32}{-125}\)

Solution

b.

La réponse est "oui" :

\(\cfrac {32}{-125}=-\cfrac {256}{1000}\)

Question

\(\cfrac {32}{24}\)

Solution

c.

La réponse est "non" :

\(\cfrac {32}{24}=\cfrac {4}{3}\)

Question

\(\cfrac {-3^2}{(-2)^3}\)

Solution

d.

La réponse est "oui" :

\(\cfrac {-3^2}{(-2)^3}=\cfrac {3^2}{2^3}=\cfrac {3^2 × 5^3}{2^3 × 5^3}= \cfrac {3^2 × 5^3}{1000}\)