Nom : ____________________________________ Classe : __________

Calculs avec des fractions — 15 minutes

SUJET A

Calculatrice interdite — Détailler les étapes et simplifier les résultats.

1. \(A=\dfrac45-\dfrac25\left(\dfrac13-3\right)\)

Corrigé

\(A=\dfrac45-\dfrac25\left(\dfrac13-\dfrac93\right)\)

\(A=\dfrac45-\dfrac25\left(\dfrac{-8}{3}\right)\)

\(A=\dfrac45+\dfrac{16}{15}\)

\(A=\dfrac{12}{15}+\dfrac{16}{15}\)

\(A=\dfrac{28}{15}\)

2. \(B=\dfrac{\dfrac34-\dfrac14}{\dfrac34+\dfrac14}\div\dfrac23\)

Corrigé

\(B=\dfrac{\dfrac34-\dfrac14}{\dfrac34+\dfrac14}\times\dfrac32\)

\(B=\dfrac{\dfrac24}{\dfrac44}\times\dfrac32\)

\(B=\dfrac12\times\dfrac32\)

\(B=\dfrac{3}{4}\)

3. \(C=\dfrac a2-\dfrac a2\times\dfrac69-\dfrac69\)

Corrigé

\(C=\dfrac a2-\dfrac a2\times\dfrac69-\dfrac69\)

\(C=\dfrac a2-\dfrac{6a}{18}-\dfrac69\)

\(C=\dfrac a2-\dfrac a3-\dfrac23\)

\(C=\dfrac{3a}{6}-\dfrac{2a}{6}-\dfrac46\)

\(C=\dfrac{a-4}{6}\)

4. \(D=\dfrac{a+\dfrac a3-\dfrac a2}{2a+\dfrac{3a}{4}+\dfrac a3}\)

Corrigé

\(D=\dfrac{\dfrac{6a+2a-3a}{6}}{\dfrac{24a+9a+4a}{12}}\)

\(D=\dfrac{\dfrac{5a}{6}}{\dfrac{37a}{12}}\)

\(D=\dfrac{5a}{6}\times\dfrac{12}{37a}\)

\(D=\dfrac{10}{37}\)