[tex]a) \frac{4}{9} \times x = \frac{1}{2} \times 54[/tex]
[tex] \frac{4x}{9} = \frac{54}{2} [/tex]
[tex] \frac{4x}{9} = 27[/tex]
[tex]4x = 9 \times 27[/tex]
[tex]4x = 243[/tex]
[tex]x = \frac{243}{4} [/tex]
[tex]x = 60.75[/tex]
[tex]b) \frac{5}{6} \times \frac{8}{15} \times x = 20[/tex]
[tex] \frac{1}{3} \times \frac{4}{3} \times x = 20[/tex]
[tex] \frac{4x}{9} = 20[/tex]
[tex]4x = 20 \times 9[/tex]
[tex]4x = 180[/tex]
[tex]x = \frac{180}{4} [/tex]
[tex]x = 45[/tex]
[tex]c)2 \frac{1}{7} \times x = \frac{2}{5} \times 50[/tex]
[tex] \frac{2 \times 7 + 1}{7} \times x = 2 \times 10[/tex]
[tex] \frac{15x}{7} = 20[/tex]
[tex]15x = 7 \times 20[/tex]
[tex]15x = 140[/tex]
[tex]x = \frac{140}{15} [/tex]
[tex]x = \frac{28}{3} [/tex]
[tex]x = 9.(3)[/tex]
[tex]d)1 \frac{3}{7} \times \frac{14}{25} \times x = 1[/tex]
[tex] \frac{1 \times 7 + 3}{7} \times \frac{14}{25} \times x = 1[/tex]
[tex] \frac{10}{7} \times \frac{14}{25} \times x = 1[/tex]
[tex]2 \times \frac{2}{5} \times x = 1[/tex]
[tex] \frac{4x}{5} = 1[/tex]
[tex]4x = 5[/tex]
[tex]x = \frac{5}{4} [/tex]
[tex]x = 1.25[/tex]
