Maths題求解答(詳細)

(c - 5 ) c
-------- + 3 = 2 - ---
6 8

(c - 5 ) c
----------* K + 3*K = 2 * K - --- * K
6 8

方程式內有兩個分數, 兩個分母是 6 與 8

1 1 4 4
--- - --- = ----- - -------
6 8 6x4 8x3

要通分母, 最小公倍數作為新的分母 = 24

6,12,18,24,30
8,16,24,32

L.C.M. of 6 and 8 is 24

2 |6, 8
------
3 4

2 * 3 * 4 = 24

K 便是 L.C.M. of 6 與 8
K = 24


(c - 5 ) c
----------* 24 + 3*24 = 2 * 24 - --- * 24
6 8

4(c – 5) + 72 = 48 – 3C

你要識計算最小公倍數 (Least Common Multiple)

另外一個例子:
a b c
--- + 13 - ---- = -----
8 9 6

方程式內有三個分數, 三個分母是8, 9 與 6
L.C.M. of 8, 9, 6 是 72
K = 72

2 |8, 9, 6
----------
3 | 4, 9, 3
---------
4, 3, 1

2 * 3 * 4 * 3 * 1 = 72
72 is divisible by 8, 9, and 6

k = 0 ( mod 24 )

Find a numberKthat can be used to eliminate the fractions in the equation by multiplying it on both sides

equation: (c-5)/6+3=2-c/8
----------------------------------------------------------------------
試找出 一個數值為K 的數字 使得以下等式兩旁同時乘上該數字可以消除等式兩旁的所有分數。

等式: (c-5)/6+3=2-c/8
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問題: [(c-5)/6+3 ] x K = [2-c/8] x K
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V
(c-5) x K/6 +3K= 2K - c x K/8
K 可以使 K/6 及K/8 為整數, 求K
(這裡應該假設了 c 為整數)