Question

ifA:B=2:3,B:C=4:5,C:D=6:7,thenA:B:C:D is

Answer 1

The best way I think I can explain this is first to find the LCM of ,  and , which, of course, is . 
Now express each of the fractions above with a denominator of . 
So, 
 
 
 . . . . . . . . . ( 1 ) 
In the last ratio, we have  as . How can we express  as ? 
Well, 
, so if we want to express this as, then 
 
So  
Therefore we can express  as  . . . . . . . . ( 2 ) 
We have that , and now we want to get it so that  is . 
So  
Hence  
Therefore we can express  as  . . . . . . . . ( 3 ) 
Collecting the three ratios ( 1 ), ( 2 ) and ( 3 ) together, we have 
A . . . 48 . . . . . B . . . .72 . . . . . C . . . 90
-- . = . ---- . . . . --- . = . ---- . . . . . -- .= .-----
B . . . 72 . . . . . C . . . .90 . . . . . D . . .105 
From which you can see that  
or, dividing by , you get in lowest terms
this will help you