小學份數數學問題－百科全書

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小學份數數學問題

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發問:

3/7 = 1/? +1/? +1/? 以上有三個不同分母, 但不能是7, 要三個分母都不同

最佳解答:

3/7 = 1/3 + 1/14 + 1/42 或 3/7 = 1/4 + 1/6 + 1/84 解釋: 3/7 = 6/14 = ... = 18/42 =... = 36/84 (擴分) = 1/?+1/?+1/? >> 嘗試 18/42 = 1/?+1/?+1/? (三個不同分母) 18/42 = (??+ ?? + ??) /42 (三個不同是分子) 如果分子 ?? 是 42 的因數，那麼 ??/42 可約至 1/? 42的因數： 1, 2, 3, 6, 7, 14, 21, 42 (但分子 ?? 不會是6, 因為分母不是7而 6/42 = 1/7) (由於分子的和是18, ?? < 18, 所以 ??不會是21 或 42) 18 = 14 + 3 + 1 所以 18/42 = (14 + 3 + 1) /42 = 14/42 + 3/42 + 1/42 = 1/3 + 1/14 + 1/42 >> 嘗試 36/84 = 1/?+1/?+1/? (三個不同分母) 36/84 = (??+ ?? + ??) /42 (三個不同是分子) 84的因數：1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 (分子不可能是12, 21, 28, 42) 36 = 21 + 14 + 1 所以 36/84 = (21 + 14 + 1) /84 = 21/84 + 14/84 + 1/84 = 1/4 + 1/6 + 1/84

其他解答:

3/7=1/6+1/3+1/5|||||It is a question about Egyptian fraction an unknown integer x that makes |3/7 - 1/x| minimum is x=2 consider 3/7 = 1/2 - 1/14 note that 1/n = 1/(n+1) + 1/n(n+1) i.e. 3/7 = 1/2 - (1/(14+1) + 1/14(14+1)) 3/7 = 1/2 - 1/15 - 1/210 i.e. the unknowns are 2, -15 and -210 2007-04-03 14:43:24 補充： others' "answers":1/3+1/5+1/6 should be = 7/10 but not 3/7 wor...|||||如果係分母無限制ge話,,,,我會放小數落去就會係: 1/10.5+ 1/21+ 1/3.5 = 3/7 (=2/21+ 1/21+ 6/3.5) (=9/21) =3/7