f.2 maths 比!

1.)
1/a : 1/b = 4 : 5
a : b = 1/4 : 1/5
a : b = (1/4) x 20 : (1/5) x 20
a : b = 5 : 4

=====
2.)
1/a : 1/b = 2/3 : 5/7
a : b = 3/2 : 7/5
a : b = (3/2) x 10 : (7/5) x 10
a : b = 15 : 14

=====
3.)
1/a : 1/b : 1/c = 2 : 3 : 4
a : b : c = 1/2 : 1/3 : 1/4
a : b : c = (1/2) x 12 : (1/3) x 12 : (1/4) x 12
a : b : c = 6 : 4 : 3
=

求 a : b

1.) 1/a : 1/b = 4 : 5

(1/a) / (1/b)=4/5
b/a=4/5
所以 a : b = 5 :4


2.) 1/a : 1/b = 2/3 : 5/7

(1/a) / (1/b) =(2/3) / (5/7)
b/a = 14/15
所以 a : b = 15 : 14


求 a : b : c

3.) 1/a : 1/b : 1/c = 2 : 3 : 4

1/a : 1/b = 2 : 3
(1/a) / (1/b) = 2/3
b/a=2/3
a : b = 3 : 2

1/b : 1/c = 3 : 4
(1/b) / (1/c) = 3/4
c/b = 3/4
b : c = 3 : 4

a : b......= 3 : 2
.....b : c = .....3 : 4
所以 a : b : c = 9 : 6 : 8

2008-11-26 17:37:47 補充：
1/b : 1/c = 3 : 4
(1/b) / (1/c) = 3/4
c/b = 3/4
b : c = 4 : 3

a : b......= 3 : 2
.....b : c = .....4 : 3
所以 a : b : c = 6 : 4 : 3

1.

圖片參考：http://codecogs.izyba.com/gif.latex?%5Cfrac%7B1%7D%7Ba%7D:%5Cfrac%7B1%7D%7Bb%7D=4:5%5C%5C%20%5Cfrac%7B%5Cfrac%7B1%7D%7Ba%7D%7D%7B%5Cfrac%7B1%7D%7Bb%7D%7D=%5Cfrac%7B4%7D%7B5%7D%5C%5C%20%5Cfrac%7Bb%7D%7Ba%7D=%5Cfrac%7B4%7D%7B5%7D%5C%5C%20a:b=5:4

2.

圖片參考：http://codecogs.izyba.com/gif.latex?%5Cfrac%7B1%7D%7Ba%7D:%5Cfrac%7B1%7D%7Bb%7D=%5Cfrac%7B2%7D%7B3%7D:%5Cfrac%7B5%7D%7B7%7D%5C%5C%20%5Cfrac%7B%5Cfrac%7B1%7D%7Ba%7D%7D%7B%5Cfrac%7B1%7D%7Bb%7D%7D=14:5%5C%5C%20%5Cfrac%7Bb%7D%7Ba%7D=14:5%5C%5C%20a:b=5:14

3.

圖片參考：http://codecogs.izyba.com/gif.latex?%5Cfrac%7B1%7D%7Ba%7D:%5Cfrac%7B1%7D%7Bb%7D=2:3%5C%5C%20%5Cfrac%7B%5Cfrac%7B1%7D%7Ba%7D%7D%7B%5Cfrac%7B1%7D%7Bb%7D%7D=2:3%5C%5C%20%5Cfrac%7Bb%7D%7Ba%7D=2:3%5C%5C%20a:b=3:2%5C%5C%20a:b=6:4


圖片參考：http://codecogs.izyba.com/gif.latex?%5Cfrac%7B1%7D%7Bb%7D:%5Cfrac%7B1%7D%7Bc%7D=3:4%5C%5C%20%5Cfrac%7B%5Cfrac%7B1%7D%7Bb%7D%7D%7B%5Cfrac%7B1%7D%7Bc%7D%7D=3:4%5C%5C%20%5Cfrac%7Bc%7D%7Bb%7D=3:4%5C%5C%20b:c=4:3


圖片參考：http://codecogs.izyba.com/gif.latex?a:b:c=6:4:3



I hope I have not made any mistakes.
Plesae feel free to ask if you have any questions.



2008-11-22 17:52:10 補充：
I am sorry that the answer to Q2 is wrong
it should be a:b=15:14

1.) 1/a : 1/b = 4 : 5
1/a / 1/b = 4/5
1/a * b = 4/5
b/a = 4/5
5b = 4a
a/b = 5/4
a : b = 5 : 4

Therefore, the ans. is a : b = 5 : 4. //

2.) 1/a : 1/b = 2/3 : 5/7
1/a / 1/b = 2/3 / 5/7
1/a * b = 2/3 * 7/5
b/a = 14/15
15b = 14a
a/b = 15/14
a : b = 15 :14

Therefore, the ans. is a : b = 15 : 14. //

3.) 1/a : 1/b : 1/c = 2 : 3 : 4

Find a : b
1/a : 1/b = 2 : 3
1/a / 1/b = 2/3
1/a *b = 2/3
b/a = 2/3
3b = 2a
a/b = 3/2
a : b = 3 : 2
Therefore, a : b = 3 : 2

Find b : c
1/b : 1/c = 3 : 4
1/b / 1/c = 3/4
1/b * c = 3/4
c/b = 3/4
4c = 3b
b/c = 4/3
b : c = 4 : 3
Therefore, b : c = 4 : 3

Since a : b = 3 : 2 and b : c = 4 : 3
a : b = 3 : 2
b : c = 4 : 3
________________
a : b : c = 6 : 4 : 3

Therefore, the ans. is a : b : c = 6 : 4 : 3. //