Question

Completar el siguiente cuadro teniendo en cuenta la propiedad fundamental de las proporciones.​

Answer 1

Respuesta:

1) 8. 2) 0.2 3) 0.6 4) -7.5 5) 1.5 6) -20 7) 0.2 8) -4

Explicación paso a paso:

1)

$\frac{6}{30} = \frac{x}{40} \\ 6 \times 40 = x \times 30 \\ 240 = 30x \\ \\ \frac{240}{30} = x \\ 8 = x$

2)

$\frac{1}{x} = \frac{1.6}{8} \\ 1 \times 8 = 1.6 \times x \\ 8 = 1.6x \\ \\ \frac{1.6}{1} \times \frac{10}{10} = \frac{16}{10} = \frac{8}{5} \\ \\ \frac{ \frac{8}{1} }{ \frac{8}{5} } = x \\ \\ \frac{1}{5} = x \\ 0.2 = x$

3)

$\frac{x}{4.5} = \frac{ 3}{0.9} \\ x \times 0.9 = 3 \times 4.5 \\ 0.9x = 13.5 \\ \\ \frac{13.5}{1} \times \frac{10}{10} = \frac{135}{10} = \frac{27}{2} \\ \frac{0.9}{1} \times \frac{10}{10} = \frac{9}{10} \\ \\ \frac{9}{10} x = \frac{27}{2} \\ \\ x = \frac{ \frac{27}{2} }{ \frac{9}{10} } \\ \\ x = \frac{3}{5} \\ x = 0.6$

4)

$\frac{1.5}{x} = \frac{ - 2.4}{12} \\ \\ \frac{1.5}{1} \times \frac{10}{10} = \frac{15}{10} = \frac{3}{2} \\ \\ \frac{ -2.4}{1} \times \frac{10}{10} = \frac{ - 24}{10} = \frac{ - 12}{5} \\ \\ \frac{3}{2} \times 12 = \frac{ - 12}{5} \times x \\ 18 = \frac{ - 12}{5} x \\ \\ \frac{ \frac{18}{1} }{ \frac{ - 12}{5} } = x \\ \\ - \frac{12}{2} = x \\ - 7.5 = x$

5)

$\frac{0.5}{0.3} = \frac{2.5}{x} \\ \frac{0.5}{1} \times \frac{10}{10} = \frac{5}{10} = \frac{1}{2} \\ \\ \frac{2.5}{1} \times \frac{10}{10} = \frac{25}{10} = \frac{5}{2} \\ \\ \frac{0.3}{1} \times \frac{10}{10} = \frac{3}{10} \\ \\ \frac{1}{2} \times x = \frac{5}{2} \times \frac{3}{10} \\ \\ \frac{x}{2} = \frac{3}{4} \\ \\ x = \frac{3}{4} \times 2 \\ x = \frac{3}{2} \\ x = 1.5$

6)

$\frac{ - 12}{x} = \frac{x}{5} \\ - 12 \times 5 = 3 \times x \\ - 60 = 3 x \\ \\ \frac{ - 60}{3} = x \\ - 20 = x$

7)

$\frac{ \frac{x}{1} }{ \frac{ - 3}{4} } = \frac{ \frac{ - 2}{15} }{ \frac{1}{2} } \\ \\ \frac{4x}{ - 3} = \frac{ - 4}{15} \\ 4x \times 15 = - 4( - 3) \\ 60x = 12 \\ x = \frac{12}{60} \\ x = \frac{1}{5} \\ x = 0.2$

8)

$\frac{0.5}{ - \frac {1}{2} } = \frac{ - 4}{x} \\ \\ \frac{0.5}{1} \times \frac{10}{10} = - \frac{5}{10} = - \frac{1}{2} \\ \\ \frac{ - \frac{1}{2} }{ - \frac{1}{2} } = \frac{ - 4}{x} \\ 1 = \frac{ - 4}{x} \\ 1 \times x = - 4 \\ x = - 4$