Calcul sur les Fractions

A) \( A = 2 - \dfrac{3}{2} = \dfrac{4}{2} - \dfrac{3}{2} = \)\( \dfrac{1}{2} \)

B) \( B = \dfrac{7}{2} + \dfrac{3}{7} = \dfrac{49}{14} + \dfrac{6}{14} = \)\( \dfrac{55}{14} \)

C) \( C = \dfrac{7}{3} - \dfrac{5}{6} + 1 = \dfrac{14}{6} - \dfrac{5}{6} + \dfrac{6}{6} = \dfrac{15}{6} = \)\( \dfrac{5}{2} \)

D) \( D = \dfrac{7}{5} - \dfrac{5}{4} = \dfrac{28}{20} - \dfrac{25}{20} = \)\( \dfrac{3}{20} \)

E) \( E = \dfrac{2}{3} - \dfrac{1}{5} = \dfrac{10}{15} - \dfrac{3}{15} = \)\( \dfrac{7}{15} \)

A) \( A = 6 - 2 \times \dfrac{5}{4} = 6 - \dfrac{10}{4} = \dfrac{12}{2} - \dfrac{5}{2} = \)\( \dfrac{7}{2} \)

B) \( B = \dfrac{9}{10} - \dfrac{2}{5} \times 3 = \dfrac{9}{10} - \dfrac{6}{5} = \dfrac{9}{10} - \dfrac{12}{10} = \)\( -\dfrac{3}{10} \)

C) \( C = \dfrac{4}{3} - \dfrac{2}{3} \times \dfrac{5}{8} = \dfrac{4}{3} - \dfrac{10}{24} = \dfrac{16}{12} - \dfrac{5}{12} = \)\( \dfrac{11}{12} \)

D) \( D = \dfrac{5}{3} \times \dfrac{2}{3} \times \dfrac{4}{7} = \dfrac{10}{9} \times \dfrac{4}{7} = \)\( \dfrac{40}{63} \)

E) \( E = \dfrac{3}{2} - \dfrac{1}{5} \times \dfrac{25}{7} = \dfrac{3}{2} - \dfrac{25}{35} = \dfrac{3}{2} - \dfrac{5}{7} = \dfrac{21}{14} - \dfrac{10}{14} = \)\( \dfrac{11}{14} \)

A) \( A = \dfrac{14}{18} \div \dfrac{2}{3} = \dfrac{14}{18} \times \dfrac{3}{2} = \dfrac{7}{9} \times \dfrac{3}{2} = \)\( \dfrac{7}{6} \)

B) \( B = \dfrac{1}{4} \div \dfrac{5}{2} = \dfrac{1}{4} \times \dfrac{2}{5} = \dfrac{2}{20} = \)\( \dfrac{1}{10} \)

C) \( C = \dfrac{9}{24} \div \dfrac{27}{36} = \dfrac{9}{24} \times \dfrac{36}{27} = \dfrac{1}{3} \times \dfrac{3}{2} = \)\( \dfrac{1}{2} \)

D) \( D = \dfrac{2}{8} \div \dfrac{3}{10} = \dfrac{1}{4} \times \dfrac{10}{3} = \dfrac{10}{12} = \)\( \dfrac{5}{6} \)

E) \( E = \dfrac{5}{6} \div \dfrac{7}{3} = \dfrac{5}{6} \times \dfrac{3}{7} = \dfrac{5}{2} \times \dfrac{1}{7} = \)\( \dfrac{5}{14} \)

A) \( A = \dfrac{7}{4} - \dfrac{3}{4} \times \left(-\dfrac{1}{9}\right) = \dfrac{7}{4} + \dfrac{3}{36} = \dfrac{7}{4} + \dfrac{1}{12} = \dfrac{21}{12} + \dfrac{1}{12} = \dfrac{22}{12} = \)\( \dfrac{11}{6} \)

B) \( B = \left(\dfrac{2}{8} - \dfrac{3}{15}\right) \div \dfrac{3}{10} = \left(\dfrac{1}{4} - \dfrac{1}{5}\right) \div \dfrac{3}{10} = \left(\dfrac{5}{20} - \dfrac{4}{20}\right) \div \dfrac{3}{10} = \dfrac{1}{20} \times \dfrac{10}{3} = \)\( \dfrac{1}{6} \)

C) \( C = \dfrac{5}{18} \times \left(\dfrac{6}{15} + \dfrac{4}{15}\right) = \dfrac{5}{18} \times \dfrac{10}{15} = \dfrac{5}{18} \times \dfrac{2}{3} = \)\( \dfrac{5}{27} \)

D) \( D = \left(4 - \dfrac{2}{3}\right) \times \left(2 - \dfrac{4}{3}\right) = \left(\dfrac{12}{3} - \dfrac{2}{3}\right) \times \left(\dfrac{6}{3} - \dfrac{4}{3}\right) = \dfrac{10}{3} \times \dfrac{2}{3} = \)\( \dfrac{20}{9} \)

E) \( E = \dfrac{2}{3} - \dfrac{5}{3} \times \left(1 - \dfrac{1}{5}\right) = \dfrac{2}{3} - \dfrac{5}{3} \times \dfrac{4}{5} = \dfrac{2}{3} - \dfrac{4}{3} = \)\( -\dfrac{2}{3} \)

A) \( A = \dfrac{\dfrac{7}{3} + \dfrac{1}{9}}{\dfrac{7}{3} - 3} = \dfrac{\dfrac{21}{9} + \dfrac{1}{9}}{\dfrac{7}{3} - \dfrac{9}{3}} = \dfrac{\dfrac{22}{9}}{-\dfrac{2}{3}} = \dfrac{22}{9} \times \left(-\dfrac{3}{2}\right) = \)\( -\dfrac{11}{3} \)

B) \( B = \dfrac{2 + \dfrac{1}{3}}{\dfrac{1}{3} - 1} = \dfrac{\dfrac{6}{3} + \dfrac{1}{3}}{\dfrac{1}{3} - \dfrac{3}{3}} = \dfrac{\dfrac{7}{3}}{-\dfrac{2}{3}} = \dfrac{7}{3} \times \left(-\dfrac{3}{2}\right) = \)\( -\dfrac{7}{2} \)

C) \( C = \dfrac{\dfrac{1}{2} + \dfrac{1}{3}}{\dfrac{1}{2} - \dfrac{1}{3}} = \dfrac{\dfrac{3}{6} + \dfrac{2}{6}}{\dfrac{3}{6} - \dfrac{2}{6}} = \dfrac{\dfrac{5}{6}}{\dfrac{1}{6}} = \dfrac{5}{6} \times 6 = \)\( 5 \)

D) \( D = 2 + \dfrac{4}{3} \div \left(-\dfrac{1}{5}\right) = 2 + \dfrac{4}{3} \times (-5) = 2 - \dfrac{20}{3} = \dfrac{6}{3} - \dfrac{20}{3} = \)\( -\dfrac{14}{3} \)

E) \( E = \dfrac{1}{1 + \dfrac{1}{1+\dfrac{1}{2}}} = \dfrac{1}{1 + \dfrac{1}{\dfrac{3}{2}}} = \dfrac{1}{1 + \dfrac{2}{3}} = \dfrac{1}{\dfrac{3}{3} + \dfrac{2}{3}} = \dfrac{1}{\dfrac{5}{3}} = \)\( \dfrac{3}{5} \)