Calculs avec des Fractions

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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