Nom : ____________________________________ Classe : __________

Calculs avec des fractions - 15 minutes - Sujet C

Calculatrice interdite - Détailler les étapes et simplifier les résultats.

1. \(A=\dfrac34-\dfrac14\left(\dfrac25-4\right)\)

Corrigé

\(A=\dfrac34-\dfrac14\left(\dfrac25-\dfrac{20}{5}\right)\)

\(A=\dfrac34-\dfrac14\left(\dfrac{-18}{5}\right)\)

\(A=\dfrac34+\dfrac{9}{10}\)

\(A=\dfrac{15}{20}+\dfrac{18}{20}\)

\(A=\dfrac{33}{20}\)

2. \(B=\dfrac{\dfrac23-\dfrac13}{\dfrac23+\dfrac13}\div\dfrac34\)

Corrigé

\(B=\dfrac{\dfrac13}{1}\times\dfrac43\)

\(B=\dfrac49\)

3. \(C=\dfrac a4-\dfrac a4\times\dfrac9{12}-\dfrac3{4}\)

Corrigé

\(C=\dfrac a4-\dfrac a4\times\dfrac34-\dfrac3{4}\)

\(C=\dfrac a4-\dfrac{3a}{16}-\dfrac3{4}\)

\(C=\dfrac{4a}{16}-\dfrac{3a}{16}-\dfrac{12}{16}\)

\(C=\dfrac{a-12}{16}\)

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

Corrigé

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

\(D=\dfrac{\dfrac{5a}{4}}{\dfrac{15a}{6}}\)

\(D=\dfrac{5a}{4}\times\dfrac{6}{15a}\)

\(D=\dfrac12\)