Question

Решите уравнение: ‪4 целых 1/6 - 3 х = 1 целая 1/2 5 целых 1/3 : (4/9 х) = 1 целая 5/7 : 3/14 Даю 50 баллов! Заранее спасибо))))

Answer 1

4 целых 1/6 - 3х = 1 целая 1/2
3х = 4 1/6 - 1 1/2 = 4 1/6 - 1 3/6 = 3 7/6 - 1 3/6 = 2 4/6 = 2 2/3 = 8/3
х = 8/3 : 3 = 8/3 * 1/3 = 8/9
х = 8/9
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Проверка: 4 1/6 - 3 * 8/9 = 1 1/2
                  4 1/6 - 8/3 = 1 1/2
                  4 1/6 - 2 2/3 = 1 1/2
                  4 1/6 - 2 4/6 = 1 1/2
                  3 7/6 - 2 4/6 = 1 1/2
                  1 3/6 = 1 1/2 - верно
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1 способ (пропорция)
5 целых 1/3 : 4/9х = 1 целая 5/7 : 3/14 
4/9х * 1 5/7 = 5 1/3 * 3/14 - свойство пропорции
4/9х * 12/7 = 16/3 * 3/14 = 16/14 = 8/7
4/9х = 8/7 : 12/7 = 8/7 * 7/12 = 8/12 = 2/3
х = 2/3 : 4/9 = 2/3 * 9/4 = (1*3)/(1*2) = 3/2 = 1 1/2
х = 1 целая 1/2

2 способ (уравнение)
5 1/3 : 4/9х = 1 5/7 :  3/14
5 1/3 : 4/9х = 12/7 * 14/3 = (4*2)/(1*1) = 8
4/9х = 5 1/3 : 8 = 16/3 * 1/8 = (2*1)/(3*1) = 2/3
х = 2/3 : 4/9 = 2/3 * 9/4 = (1*3)/(1*2) = 3/2 = 1 1/2
х = 1 целая 1/2