Nom : ____________________________________ Classe : __________

Calculs avec des fractions - 15 minutes - Sujet D

Calculatrice interdite - Détailler les étapes et simplifier les résultats.

1. \(A=\dfrac78-\dfrac18\left(\dfrac13-3\right)\)

Corrigé

\(A=\dfrac78-\dfrac18\left(\dfrac13-\dfrac{9}{3}\right)\)

\(A=\dfrac78-\dfrac18\left(\dfrac{-8}{3}\right)\)

\(A=\dfrac78+\dfrac{8}{24}\)

\(A=\dfrac78+\dfrac13\)

\(A=\dfrac{21}{24}+\dfrac{8}{24}\)

\(A=\dfrac{29}{24}\)

2. \(B=\dfrac{\dfrac35-\dfrac15}{\dfrac35+\dfrac15}\div\dfrac56\)

Corrigé

\(B=\dfrac{\dfrac25}{\dfrac45}\times\dfrac65\)

\(B=\dfrac12\times\dfrac65\)

\(B=\dfrac{3}{5}\)

3. \(C=\dfrac a5-\dfrac a5\times\dfrac{15}{20}-\dfrac{3}{4}\)

Corrigé

\(C=\dfrac a5-\dfrac a5\times\dfrac{3}{4}-\dfrac{3}{4}\)

\(C=\dfrac a5-\dfrac{3a}{20}-\dfrac{15}{20}\)

\(C=\dfrac{4a}{20}-\dfrac{3a}{20}-\dfrac{15}{20}\)

\(C=\dfrac{a-15}{20}\)

4. \(D=\dfrac{a+\dfrac a6-\dfrac a3}{2a+\dfrac a4+\dfrac a2}\)

Corrigé

\(D=\dfrac{\dfrac{6a+a-2a}{6}}{\dfrac{8a+a+2a}{4}}\)

\(D=\dfrac{\dfrac{5a}{6}}{\dfrac{11a}{4}}\)

\(D=\dfrac{5a}{6}\times\dfrac{4}{11a}\)

\(D=\dfrac{10}{33}\)