[tex]1) \frac{a}{b} = \frac{3}{8} \: | \times \frac{4}{3} [/tex]
[tex] \frac{4a}{3b} = \frac{ 12 }{24} [/tex]
[tex] \frac{4a}{3b} = \frac{ 1 }{2} [/tex]
[tex]2) \frac{25x}{2y} = 6.25[/tex]
[tex] \frac{25x}{2y} = \frac{625}{100} [/tex]
[tex] \frac{25x}{2y} = \frac{125}{20} [/tex]
[tex] \frac{25x}{2y} = \frac{25}{4} [/tex]
[tex]25x \times 4 = 2y \times 25[/tex]
[tex]100x = 50y \: | \div x[/tex]
[tex] \frac{50y}{x} = 100[/tex]
[tex] \frac{y}{x} = \frac{100}{50} [/tex]
[tex] \frac{y}{x} = 2[/tex]
[tex]3) \frac{x}{y} = 0.5[/tex]
[tex] \frac{x}{y} = \frac{5}{10} = \frac{1}{2} [/tex]
[tex]y = 2x[/tex]
[tex] \frac{2x + 3y}{5x - y} = \frac{2x + 3 \times 2x}{5x - 2x} = \frac{2x + 6x}{3x} = \frac{8x}{3x} = \frac{8}{3} [/tex]
[tex]4) \frac{x}{y} = 0.(6)[/tex]
[tex] \frac{x}{y} = \frac{6}{9} = \frac{2}{3} [/tex]
[tex]3x = 2y[/tex]
[tex]x = \frac{2y}{3} [/tex]
[tex] \frac{x}{x + y} = \frac{ \frac{2y}{3} }{ \frac{2y}{3} + y} = \frac{ \frac{2y}{3} }{ \frac{2y}{3} + \frac{3y}{3} } = \frac{ \frac{2y}{3} }{ \frac{2y + 3y}{3} } = \frac{ \frac{2y}{3} }{ \frac{5y}{3} } = \frac{2y}{5y} = \frac{2}{5} [/tex]
