\[ \frac{2}{3} \times \frac{5}{7} = \frac{2 \times 5}{3 \times 7} = \frac{10}{21} \]

\[ \frac{4}{5} \div \frac{2}{3} = \frac{4}{5} \times \frac{3}{2} = \frac{12}{10} = \frac{6}{5} \]

\[ \frac{15}{8} \times \frac{4}{25} = \frac{15 \times 4}{8 \times 25} = \frac{60}{200} = \frac{3}{10} \]

Ou avec simplification préalable :

\[ \frac{15}{8} \times \frac{4}{25} = \frac{3 \times \cancel{5}}{8} \times \frac{4}{5 \times \cancel{5}} = \frac{3 \times \cancel{4}}{2 \times \cancel{4} \times 5} = \frac{3}{10} \]

\[ \frac{21}{10} \div \frac{14}{15} = \frac{21}{10} \times \frac{15}{14} = \frac{315}{140} = \frac{63}{28} = \frac{9}{4} \]

Ou avec simplification préalable :

\[ \frac{\cancel{21}^{3}}{10} \times \frac{15}{\cancel{14}^{2}} = \frac{3 \times \cancel{15}^{3}}{\cancel{10}^{2} \times 2} = \frac{9}{4} \]

\[ \frac{3}{5} \times \frac{10}{9} \times \frac{6}{4} = \frac{3 \times 10 \times 6}{5 \times 9 \times 4} = \frac{180}{180} = 1 \]

Ou avec simplification :

\[ \frac{\cancel{3}}{5} \times \frac{10}{\cancel{9}^{3}} \times \frac{\cancel{6}^{3}}{\cancel{4}^{2}} = \frac{1}{\cancel{5}} \times \frac{\cancel{10}^{2}}{3} \times \frac{3}{2} = \frac{2 \times \cancel{3}}{\cancel{3} \times 2} = 1 \]

\[ 8 \div \frac{2}{5} = 8 \times \frac{5}{2} = \frac{40}{2} = 20 \]

\[ \frac{-3}{4} \times \frac{2}{-5} = \frac{(-3) \times 2}{4 \times (-5)} = \frac{-6}{-20} = \frac{3}{10} \]

Règle des signes : – × – = +

\[ \frac{7}{-3} \div \frac{-14}{9} = \frac{7}{-3} \times \frac{9}{-14} = \frac{63}{42} = \frac{3}{2} \]

Simplification :

\[ \frac{\cancel{7}}{-3} \times \frac{9}{-2 \times \cancel{7}} = \frac{9}{6} = \frac{3}{2} \]

\[ \frac{3}{4} \times \frac{2}{3} = \frac{\cancel{3}}{4} \times \frac{2}{\cancel{3}} = \frac{2}{4} = \frac{1}{2} \]

Ahmed a mangé la moitié de la pizza entière.

\[ \frac{15}{2} \div \frac{3}{4} = \frac{15}{2} \times \frac{4}{3} = \frac{60}{6} = 10 \]

On peut remplir 10 bouteilles.