a:b= 9 : 6 和 b:c= 9 : 7 , 求 a: b: c

a:b= 9 : 6 和 b:c= 9 : 7 , 求 a: b: c

b:c = 9:7
b/c = 9/7
b = 9c/7 ........ (1)

a:b = 9/6
a/b = 9/6
a = 9b/6
a = 9(9c/7)/6 ............. 拫據 (1)
a = 81c/42 .......(3)

根據 (1) 和 (3)

a:b:c
= 81c/42:9c/7:c
= 81/42:9/7:1
= 81/42:9(6)/42:42/42
= 81:54:42

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1/a:1/b= 3 : 9 , 求 a: b

1/a:1/b = 3:9
(1/a)/(1/b) = 3/9
(1/a)/(1/b) = 1/3
(1/a)*3 = (1/b)*1
3/a = 1/b
3/1 = a/b
所以 a:b = 3:1

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a:b:c= 4 : 10 : 4 , 求 1/a:1/b:1/c

b:c = 10:4
b:c = 5:2
b/c = 5/2
b = 5c/2 ................... (1)

a:c = 4:4
a:c = 1:1
a/c = 1/1
a = c ........................ (2)

根據 (1) 和 (2)：

1/a:1/b:1/c
= 1/c:1/(5c/2):1/c
= 1/c: 2/5c: 1/c
= (1)(1/c): (2/5)(1/c): (1)(1/c)
= 1: 2/5: 1
= 5: 2: 5

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1/a:1/b:1/c= 10 : 5 : 8 , 求 a:b:c

1/b: 1/c = 5:8
(1/b)/(1/c) = 5/8
8(1/b) = 5(1/c)
8/b = 5/c
8c = 5b
b = 8c/5 ................................. (1)

1/a: 1/c = 10:8
1/a: 1/c = 5:4
(1/a)/(1/c) = 5/4
4(1/a) = 5(1/c)
4/a = 5/c
4c = 5a
a = 4c/5 .................................. (2)

根據 (1) 和 (2)：
a: b: c
= 4c/5: 8c/5: c
= 4/5: 8/5: 1
= 4: 8: 5

第一題答案應要約簡才對
Ans:27:18:14

1, a:b = 3;
2, = 1/4 : 1/10 : 1/4
3, = 1/10 : 1/5 : 1/8