Multiplicación y división de fracciones - problemas difíciles y soluciones

Solución:
[tex]\frac{5}{27} \times \frac{9}{25}=\frac{5}{9 \times 3} \times \frac{9}{5 \times 5}=\frac{5 \times 9}{9 \times 3 \times 5 \times 5}=\frac{1}{15}[/tex]

Solución:
[tex]\frac{40}{25} \times \frac{90}{15}=\frac{8 \times 5}{5 \times 5} \times \frac{6 \times 15}{15}=\frac{8}{5} \times 6=\frac{48}{5}[/tex]

Solución:
[tex]\frac{12}{25} \times \frac{15}{14}=\frac{12 \times 15}{25 \times 14}=\frac{3 \times 4 \times 3 \times 5}{5 \times 5 \times 7 \times 2}=\frac{3 \times 2 \times 2 \times 3}{5 \times 7 \times 2}=\frac{3 \times 2 \times 3}{5 \times 7}=\frac{18}{35}[/tex]

Solución:
[tex]\frac{5}{13} \times \frac{26}{20}=\frac{5 \times 26}{13 \times 20}=\frac{5 \times 2 \times 13}{13 \times 2 \times 10}=\frac{5}{10}=\frac{1}{2}[/tex]

Solución:
[tex]\frac{24}{25} \cdot \frac{75}{18}=\frac{24}{25} \cdot \frac{75}{18}=\frac{4 \cdot 6}{25} \cdot \frac{3 \cdot 25}{3 \cdot 6}=\frac{4}{3}\cdot 3=4[/tex]

Solución:
[tex]\frac{40}{27} \times \frac{18}{5}=\frac{40}{5} \times \frac{18}{27}=\frac{5 \times 8}{5} \times \frac{2 \times 9}{3 \times 9}=8 \times \frac{2}{3}=\frac{16}{3}[/tex]

Solución:
[tex]\frac{8}{15}:\frac{4}{5}=\frac{8}{15} \times \frac{5}{4}=\frac{8}{4} \times \frac{5}{15}=2 \times \frac{1}{3}=\frac{2}{3}[/tex]

Solución:
[tex]\frac{18}{25}:\frac{27}{35}=\frac{18}{25} \times \frac{35}{27}=\frac{2\times 9}{5 \times 5} \times \frac{5 \times 7}{3 \times 9}=\frac{2}{5} \times \frac{7}{3}=\frac{2 \times 7}{3 \times 5}=\frac{14}{15}[/tex]

Solución:
[tex]\frac{100}{49}:\frac{25}{7}=\frac{100}{49}\cdot \frac{7}{25}=\frac{25 \cdot 4}{7 \cdot 7}\cdot \frac{7}{25}=\frac{4}{7}[/tex]

Solución:
[tex]\frac{5}{8} \times \frac{3}{4} \times \frac{12}{15}=\frac{5 \times 3 \times 12}{8 \times 4 \times 15}=\frac{5 \times 3 \times 4 \times 3}{8 \times 4 \times 3 \times 5}=\frac{3}{8}[/tex]

Solución:
[tex]\frac{5}{6}:\frac{2}{3}=\frac{5}{6} \times \frac{3}{2}=\frac{5 \times 3}{2 \times 6}=\frac{5 \times 3}{2 \times 2 \times 3}=\frac{5}{4}[/tex]

Solución:
[tex]\frac{2}{3} \times \frac{3}{4} : \frac{7}{2} = \frac{2}{4} : \frac{7}{2} = \frac{1}{2} \times \frac{2}{7} = \frac{1}{7}[/tex]

Solución:
[tex]\frac{2}{3} \times \frac{5}{12} \times \frac{6}{10} \times \frac{9}{11} = \frac{2 \times 5 \times 6 \times 9}{3 \times 12 \times 10 \times 11} = \frac{10 \times 6 \times 9}{10 \times 3 \times 3 \times 4 \times 11} = \frac{6 \times 9}{9 \times 44} = \frac{6}{44} = \frac{3}{22}[/tex]

Solución:
[tex]\frac{18}{19} \times \frac{38}{72} = \frac{18 \times 38}{19 \times 72}=\frac{18 \times 2 \times 19}{19 \times 4 \times 18}=\frac{2}{4}=\frac{1}{2}[/tex]

Solución:
[tex]\frac{5}{17} : \frac{8}{17} \times 40 = \frac{5}{17} \times \frac{17}{8} \times 40 = \frac{5}{8} \times 40 = 5 \times \frac{40}{8} = 5 \times 5 = 25[/tex]

Solución:
[tex]\frac{20}{7} : \frac{15}{14} = \frac{20}{7} \times \frac{14}{15} = \frac{20}{15} \times \frac{14}{7} = \frac{4\times 5}{3\times 5} \times \frac{2 \times 7}{7} = \frac{4}{3} \times 2 = \frac{8}{3}[/tex]

Solución:
[tex]\frac{5}{16} \times \frac{8}{13} \times \frac{26}{25} = \frac{5 \times 8 \times 26}{25 \times 13 \times 16} = \frac{5}{25} \times \frac{8 \times 26}{13 \times 16} = \frac{1}{5} \times \frac{8 \times 2 \times 13}{13 \times 8 \times 2} = \frac{1}{5} \times 1 = \frac{1}{5}[/tex]

Solución:
[tex]\frac{27}{13} \times \frac{26}{25} \times \frac{20}{18} = \frac{27 \times 26 \times 20}{13 \times 25 \times 18} = \frac{3 \times 9 \times 2 \times 13 \times 4 \times 5}{13 \times 5 \times 5 \times 2 \times 9}=\frac{9 \times 13 \times 2 \times 5 \times 3 \times 4}{9 \times 13 \times 2 \times 5 \times 5} = \frac{12}{5}[/tex]

Solución:
[tex]\frac{5}{18} \times \frac{9}{14} : \frac{20}{21} = \frac{5}{18} \times \frac{9}{14} \times \frac{21}{20} = \frac{5}{2 \times 9} \times \frac{9}{2 \times 7} \times \frac{3 \times 7}{5 \times 4}= \frac{1}{2} \times \frac{1}{2} \times \frac{3}{4} = \frac{3}{16}[/tex]

Solución:
[tex]\frac{1}{2} : \frac{9}{10} \times \frac{15}{5} = \frac{1}{2} \times \frac{10}{9} \times 3 = \frac{5}{9} \times 3 = \frac{5}{3}[/tex]

Solución:
[tex]\frac{16}{27} \times \frac{81}{4} = \frac{16}{4} \times \frac{81}{27} = 4 \times 3 = 12[/tex]

Solución:
[tex]\frac{8}{19} \times \frac{38}{7} \times \frac{14}{16} = \frac{8}{16} \times \frac{38}{19} \times \frac{14}{7} = \frac{1}{2} \times 2 \times 2 = 2[/tex]

Solución:
[tex]\frac{17}{34} \times \frac{15}{7} \times \frac{20}{14} = \frac{1}{2} \times \frac{15}{25} \times \frac{14}{7} = \frac{1}{2} \times \frac{3}{5} \times 2 = \frac{3}{5}[/tex]

Solución:
[tex]\frac{2}{15} \times \frac{85}{51} = \frac{2}{3 \times 5} \times \frac{5 \times 17}{3 \times 17} = \frac{2}{3 \times 5} \times \frac{5}{3} = \frac{2}{9}[/tex]

Solución:
[tex]\frac{3}{8} : \frac{1}{2} \times \frac{17}{51} = \frac{3}{8} \times 2 \times \frac{17}{3 \times 17} = \frac{3}{4} \times \frac{1}{3} = \frac{1}{4}[/tex]

Solución:
[tex]\frac{7}{121} \times \frac{22}{14} \times \frac{8}{3} = \frac{7}{14} \times \frac{22}{121} \times \frac{8}{3} = \frac{1}{2} \times \frac{2}{11} \times \frac{8}{3} = \frac{8}{33}[/tex]