Solution :

1. \( \frac{4}{6} + \frac{5}{6} = \frac{9}{6} = \frac{3}{2} \)
2. \( \frac{14}{24} + \frac{9}{24} = \frac{23}{24} \)
3. \( \frac{9}{4} + \frac{3}{5} = \frac{45}{20} + \frac{12}{20} = \frac{57}{20} \)

Solution :

1. \( \frac{25}{35} – \frac{14}{35} = \frac{11}{35} \)
2. \( \frac{11}{8} – \frac{6}{8} = \frac{5}{8} \)
3. \( \frac{10}{3} – \frac{7}{5} = \frac{50}{15} – \frac{21}{15} = \frac{29}{15} \)

Solution :

1. \( \frac{30}{45} = \frac{2}{3} \)
2. \( \frac{112}{168} = \frac{2}{3} \)
3. \( \frac{5}{2} \times \frac{4}{3} = \frac{20}{6} = \frac{10}{3} \)

Solution :

1. \( \frac{5}{6} \times \frac{4}{15} = \frac{20}{90} = \frac{2}{9} \)
2. \( \frac{12}{25} \times \frac{5}{8} = \frac{60}{200} = \frac{3}{10} \)
3. \( 3 \times \frac{7}{9} = \frac{21}{9} = \frac{7}{3} \)

Solution :

1. \( \frac{1}{2} + \frac{6}{12} = \frac{1}{2} + \frac{1}{2} = 1 \)
2. \( \frac{5}{6} – \frac{5}{6} = 0 \)
3. \( (\frac{4}{10} + \frac{1}{10}) \times \frac{4}{3} = \frac{5}{10} \times \frac{4}{3} = \frac{20}{30} = \frac{2}{3} \)

Solution :

1. \( \frac{3}{4} + \frac{3}{8} = \frac{6}{8} + \frac{3}{8} = \frac{9}{8} \)
2. \( \frac{6}{5} \times \frac{5}{6} = 1 \)
3. \( \frac{5}{2} \times 4 = 10 \)

Solution :

Soit \( x \) la capacité totale :

\( \frac{3}{4}x + 12 = \frac{5}{6}x \)

\( 12 = \frac{5}{6}x – \frac{3}{4}x = \frac{10}{12}x – \frac{9}{12}x = \frac{1}{12}x \)

\( x = 12 \times 12 = 144 \) litres

Solution :

1. \( \frac{3 \times 5}{4 \times 7} \times \frac{2 \times 7}{5 \times 5} = \frac{3 \times 2}{4 \times 5} = \frac{6}{20} = \frac{3}{10} \)
2. \( \frac{24}{35} \times \frac{21}{16} = \frac{3 \times 8}{5 \times 7} \times \frac{3 \times 7}{2 \times 8} = \frac{3 \times 3}{5 \times 2} = \frac{9}{10} \)
3. \( \frac{2 \times 9}{7 \times 7} \times \frac{7}{3 \times 4} \times \frac{2 \times 7}{9} = \frac{2 \times 2}{7 \times 3} = \frac{4}{21} \)

Solution :

1. \( \frac{7}{8} = 0.875 \) et \( \frac{8}{9} ≈ 0.888… \) donc \( \frac{7}{8} < \frac{8}{9} \)
2. \( \frac{5}{6} ≈ 0.833… \) et \( \frac{7}{9} ≈ 0.777… \) donc \( \frac{5}{6} > \frac{7}{9} \)
3. \( \frac{12}{5} = 2.4 \) donc \( = \)

Solution :

Numérateur : \( \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \)

Dénominateur : \( \frac{3}{12} – \frac{2}{12} = \frac{1}{12} \)

Première fraction : \( \frac{5/6}{1/12} = \frac{5}{6} \times 12 = 10 \)

Deuxième fraction : \( \frac{2/5}{3/10} = \frac{2}{5} \times \frac{10}{3} = \frac{20}{15} = \frac{4}{3} \)

Résultat final : \( 10 \times \frac{4}{3} = \frac{40}{3} \)