х : 4/9 = 0,5 : 1/3

1/3х = 4/9 * 5/10

1/3х = 20/90 = 2/9

х = 2/9 : 1/3

х = 2/9 * 3/1

х = 2/3

Проверка: 2/3 : 4/9 = 5/10 : 1/3

                  2/3 * 9/4 = 5/10 * 3/1

                  3/2 = 15/10

                  1 1/2 = 1 5/10

                   1,5 = 1,5