Calcolare un termine incognito di una proporzione

258)

12/5 : x = x : 3/20;

il prodotto dei medi è uguale al prodotto degli estremi;

x^2 = (12 / 5) * (3 / 20);

x^2 = 12 * 3 / (5 * 20) ; si semplificano per 4 il 12 con il 20;

x^2 = 3 * 3 / (5 * 5) = 9/25;

x = radice quadrata(9/25) ;

x = 3/5;

1/2 : 3/5 = 3/5 : 3/20.

2/25 : x = x : 2/9;

x^2 = 2/25 * 2/9 = 4 / 225;

x = radice quadrata(4/225) = 2/15;

2/25 : 2/15 = 2/15 : 2/9.

Ciao @miry27

175/1

$\small \dfrac{1}{4} : x = \dfrac{1}{2} : \dfrac{2}{3}$

$\small x= \dfrac{1}{\cancel4_2}·\dfrac{\cancel2^1}{3} : \dfrac{1}{2}$

$\small x= \dfrac{1}{\cancel2_1}·\dfrac{1}{3} ·\dfrac{\cancel2^1}{1}$

$\small x= \dfrac{1}{3}$

175/2

$\small \dfrac{7}{3} : 1 = x : \dfrac{15}{4}$

$\small x= \dfrac{7}{\cancel3_1}·\dfrac{\cancel{15}^5}{4} : \cancel1$

$\small x= 7·\dfrac{5}{4}$

$\small x= \dfrac{35}{4}$

175/3

$\small 4 : x = \dfrac{8}{7} : \dfrac{3}{14}$

$\small x= \cancel4^2·\dfrac{3}{\cancel{14}_7} : \dfrac{8}{7}$

$\small x= 2·\dfrac{3}{\cancel7_1}·\dfrac{\cancel7^1}{8}$

$\small x= \cancel2^1·3·\dfrac{1}{\cancel8_4}$

$\small x= \dfrac{3}{4}$

=========================================================

197

$\small 5 : 10 = x : 60$

$\small x= \dfrac{5×\cancel{60}^6}{\cancel{10}_1}$

$\small x= 5×6 = 30\,km$

198

$\small 2 : 1 = x : 1,2$

$\small x= \dfrac{2×1,2}{1}$

$\small x= 2,4\,cm.$

180/1

$\small \dfrac{2}{3} : \dfrac{25}{18} = \dfrac{2}{5} : x$

$\small x= \dfrac{\cancel{25}^5}{\cancel{18}_9}·\dfrac{\cancel2^1}{\cancel5_1} : \dfrac{2}{3}$

$\small x= \dfrac{5}{\cancel9_3}·\dfrac{1}{1}·\dfrac{\cancel3^1}{2}$

$\small x= \dfrac{5}{3}·\dfrac{1}{2}$

$\small x= \dfrac{5}{6}$

180/2

$\small \dfrac{5}{7} : \dfrac{2}{3} = \dfrac{3}{4} : x$

$\small x= \dfrac{\cancel2^1}{\cancel3_1}·\dfrac{\cancel3^1}{\cancel4_2} : \dfrac{5}{7}$

$\small x= \dfrac{1}{1}·\dfrac{1}{2}·\dfrac{7}{5}$

$\small x= \dfrac{7}{10}$

180/3

$\small 2 : \dfrac{20}{9} = 9 : x$

$\small x= \dfrac{20}{\cancel9_1}·\cancel9^1 : 2$

$\small x= \dfrac{\cancel{20}^{10}}{1}·1·\dfrac{1}{\cancel2_1}$

$\small x= 10·1$

$\small x= 10$

258/1

$\small \dfrac{12}{5} : x = x : \dfrac{3}{20}$

moltiplica i medi e gli estremi come segue:

$\small x·x = \dfrac{\cancel{12}^3}{5}·\dfrac{3}{\cancel{20}_5}$

$\small x^2 = \dfrac{3}{5}·\dfrac{3}{5}$

$\small x^2 = \dfrac{9}{25}$

radice quadrata di ambo le parti:

$\small \sqrt{x^2} = \sqrt{\dfrac{9}{25}}$

$\small x= \dfrac{3}{5}$

258/2

$\small \dfrac{2}{25} : x = x : \dfrac{2}{9}$

moltiplica i medi e gli estremi come segue:

$\small x·x = \dfrac{2}{25}·\dfrac{2}{9}$

$\small x^2 = \dfrac{4}{225}$

radice quadrata di ambo le parti:

$\small \sqrt{x^2} = \sqrt{\dfrac{4}{225}}$

$\small x= \dfrac{2}{15}$