Multiplicación y división de fracciones - problemas y soluciones

Solución:
1 es la identidad multiplicativa, por lo que cualquier número, multiplicado por 1, permanece sin cambios.

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

Solución:
[tex]\frac{1}{3} \times 9=\frac{1}{3} \times 3 \times 3=\frac{3}{3} \times 3=1 \times 3=3[/tex]

Solución:
[tex]\frac{5}{6} \times 2 \times \frac{6}{5}=\frac{5}{6} \times \frac{6}{5} \times 2=\frac{5}{5} \times \frac{6}{6} \times 2=1 \times 1 \times 2=2[/tex]

Solución:
[tex]\frac{1}{5} \times 25=\frac{1}{5} \times 5 \times 5=\frac{5}{5} \times 5=1 \times 5=5[/tex]

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

Solución:
[tex]\frac{3}{2} \times 6 = 3 \times \frac{1}{2} \times 6=3 \times \frac{6}{2}=3 \times \frac{3 \times 2}{2}=3 \times 3=9[/tex]

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

Solución:
[tex]\frac{5}{7} \times \frac{7}{2}=\frac{5}{2} \times \frac{7}{7}=\frac{5}{2} \times 1 = \frac{5}{2}[/tex]

Solución:
[tex]\frac{18}{19} \times \frac{19}{6} = \frac{18}{6} \times \frac{19}{19} = 3 \times 1 = 3[/tex]

Solución:
[tex]3 \times \frac{4}{13} = \frac{3 \times 4}{13} = \frac{12}{13}[/tex]

Solución:
[tex]\frac{5}{18} \times \frac{3}{5} = \frac{5}{5} \times \frac{3}{18} = 1 \times \frac{1}{6} = \frac{1}{6}[/tex]

Solución:
[tex]\frac{8}{17} \times 34 = \frac{8}{17} \times 17 \times 2 = 8 \times 2 = 16[/tex]

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

Solución:
[tex]\frac{15}{16} \times \frac{8}{1} = \frac{15}{16} \times 8 = 15 \times \frac{8}{16} = 15 \times \frac{1}{2} = \frac{15}{2}[/tex]

Solución:
[tex]\frac{1}{2} : \frac{5}{2} = \frac{1}{2} \times \frac{2}{5} = \frac{1}{5} \times \frac{2}{2} = \frac{1}{5}[/tex]

Solución:
[tex]\frac{5}{7} : \frac{5}{4} = \frac{5}{7} \times \frac{4}{5} = \frac{4}{7} \times \frac{5}{5} = \frac{4}{7}[/tex]

Solución:
[tex]\frac{3}{8} : \frac{8}{9} = \frac{3}{8} \times \frac{9}{8} = \frac{3 \times 9}{8 \times 8} = \frac{27}{64}[/tex]

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

Solución:
[tex]\frac{19}{7} : \frac{25}{7} \times 5 = \frac{19}{7} \times \frac{7}{25} \times 5 = 19 \times \frac{7}{7} \times \frac{5}{25} = 19 \times 1 \times \frac{1}{5} = \frac{19}{5}[/tex]

Solución:
[tex]\frac{15}{21} : \frac{40}{7} = \frac{3 \cdot 5}{3 \cdot 7} \times \frac{7}{40} = \frac{5}{7} \times \frac{7}{40} = \frac{5}{40} = \frac{1}{8}[/tex]

Solución:
[tex]\frac{80}{18} : \frac{5}{9} = \frac{2 \cdot 40}{2 \cdot 9} \times \frac{9}{5} = \frac{40}{9} \times \frac{9}{5} = \frac{40}{5} = 8[/tex]

Solución:
[tex]\frac{24}{35} : \frac{8}{7} = \frac{24:8}{35:7} = \frac{3}{5}[/tex]

Solución:
[tex]\frac{6}{25} \times \frac{15}{9} = \frac{2 \times 3}{5 \times 5} \times \frac{3 \times 5}{3 \times 3} = \frac{2}{5} \times \frac{3}{3} = \frac{2}{5} \times 1 = \frac{2}{5}[/tex]