Напишите дроби 1/3,1/5,1/7,1/9,1/11 в виде суммы аликвотных дробей с разными знаменателями

Question

Напишите дроби 1/3,1/5,1/7,1/9,1/11 в виде суммы аликвотных дробей с разными знаменателями

Answer 1

1/3+1/5 = 8/15
1/3+1/7 = 10/21
1/3+1/9 = 4/9
1/3+1/11 = 14/33
1/5+1/7 = 12/35
1/5+1/9 = 14/45
1/5+1/11 = 16/55
1/7+1/9 = 16/63
1/7+1/11 = 18/77
1/9+1/11 = 20/99

Comments

1/3 = (1*4) / (3*4) = 4/12 = 3/12 + 1/12 = 1/4 + 1/121/5 = (1*6) / (5*6) = 6/30 = 5/30 + 1/30 = 1/6 + 1/301/7 = (1*10) / (7*10) = 10/70 = 7/70 + 2/70 + 1/70 = 1/10 + 1/35 + 1/701/9 = (1*4) / (9*4) = 4/36 = 3/36 + 1/36 = 1/12 + 1/361/11 = (1*6) / (11*6) = 6/66 = 3/66 + 2/66 + 1/66 = 1/22 + 1/33 + 1/66