[tex]a) \frac{3x}{28} = \frac{4.5}{4} [/tex]
[tex]4 \times 3x = 28 \times 4.5[/tex]
[tex]12x = 126[/tex]
[tex]x = \frac{126}{12} [/tex]
[tex]x = \frac{63}{6} [/tex]
[tex]x = \frac{21}{2} [/tex]
[tex]x = 10.5[/tex]
[tex]b) \frac{2x}{2 \frac{1}{3} } = \frac{9}{ 5\frac{1}{4} } [/tex]
[tex] \frac{2x}{ \frac{2 \times 3 + 1}{3} } = \frac{9}{ \frac{5 \times 4 + 1}{4} } [/tex]
[tex] \frac{2x}{ \frac{7}{3} } = \frac{9}{ \frac{21}{4} } [/tex]
[tex]2x \times \frac{21}{4} = 9 \times \frac{7}{3} [/tex]
[tex] \frac{42x}{4} = \frac{63}{3} [/tex]
[tex] \frac{42x}{4} = 21[/tex]
[tex]42x = 4 \times 21[/tex]
[tex]42x = 84[/tex]
[tex]x = \frac{84}{42} [/tex]
[tex]x = 2[/tex]
[tex]c) \frac{0.3}{0.4} = \frac{1.35}{0.3x} [/tex]
[tex] \frac{ \frac{3}{10} }{ \frac{4}{10} } = \frac{ \frac{135}{100} }{ \frac{3x}{10} } [/tex]
[tex] \frac{3}{4} = \frac{ \frac{27}{20} }{ \frac{3x}{10} } [/tex]
[tex] \frac{3}{4} = \frac{27}{20} \times \frac{10}{3x} [/tex]
[tex] \frac{3}{4} = \frac{27}{2} \times \frac{1}{3x} [/tex]
[tex] \frac{3}{4} = \frac{27}{6x} [/tex]
[tex]3 \times 6x = 4 \times 27[/tex]
[tex]18x = 108[/tex]
[tex]x = \frac{108}{18} [/tex]
[tex]x = \frac{54}{9} [/tex]
[tex]x = 6[/tex]
[tex]d) \frac{2x}{ \frac{2}{15} } = \frac{ \frac{1}{15} }{0.2} [/tex]
[tex] \frac{2x}{ \frac{2}{15} } = \frac{ \frac{1}{15} }{ \frac{2}{10} } [/tex]
[tex]2x \times \frac{15}{2} = \frac{1}{15} \times \frac{10}{2} [/tex]
[tex] \frac{30x}{2} = \frac{1}{15} \times 5[/tex]
[tex] \frac{30x}{2} = \frac{5}{15} [/tex]
[tex]30x \times 15 = 2 \times 5[/tex]
[tex]450x = 10[/tex]
[tex]x = \frac{10}{450} [/tex]
[tex]x = \frac{1}{45} [/tex]
[tex]e) \frac{7x}{42} = \frac{15}{9} [/tex]
[tex]7x \times 9 = 42 \times 15[/tex]
[tex]63x = 630[/tex]
[tex]x = \frac{630}{63} [/tex]
[tex]x = 10[/tex]
[tex]f) \frac{4x}{31} = \frac{44}{41} [/tex]
[tex]4x \times 41 = 31 \times 44[/tex]
[tex]164x = 1364[/tex]
[tex]x = \frac{1364}{164} [/tex]
[tex]x = \frac{682}{82} [/tex]
[tex]x = \frac{341}{41} [/tex]
[tex]g) \frac{ \frac{1}{6} }{2 \frac{1}{3} } = \frac{3.25x}{1.3} [/tex]
[tex] \frac{ \frac{1}{6} }{ \frac{2 \times 3 + 1}{3} } = \frac{ \frac{325x}{100} }{ \frac{13}{10} } [/tex]
[tex] \frac{ \frac{1}{6} }{ \frac{7}{3} } = \frac{ \frac{65x}{20} }{ \frac{13}{10} } [/tex]
[tex] \frac{1}{6} \times \frac{3}{7} = \frac{ \frac{13x}{4} }{ \frac{13}{10} } [/tex]
[tex] \frac{3}{42} = \frac{13x}{4} \times \frac{10}{13} [/tex]
[tex] \frac{1}{14} = \frac{x}{2} \times 5[/tex]
[tex] \frac{1}{14} = \frac{5x}{2} [/tex]
[tex]5x \times 14 = 1 \times 2[/tex]
[tex]70x = 2[/tex]
[tex]x = \frac{2}{70} [/tex]
[tex]x = \frac{1}{35} [/tex]
