State True or false.The ratio

11:14
,

17:21
,

5:7
,(2:3)
is in ascending order.

Question

State True or false.The ratio

11:14
   ,
    
     17:21
   ,
    
     5:7
   ,(2:3)
  is in ascending order.

Accepted Answer

It is given the ratio is

11:14
   ,
    
     17:21
   ,
    
     5:7
   ,(2:3)
 .The LCM of

14,21,7,3
  is

42
 .Make the numbers 1114,1721,57,23 with the same denominator

42
 .Therefore,

11
      
       14
     
     =
      
       11×3
      
       14×3

=
      
       33
      
       42

For the ratio 17:21,

17
      
       21
     
     =
      
       17×2
      
       21×2

=
      
       34
      
       42

For the ratio 5:7,

5
      7
     
     =
      
       5×6
      
       7×6

=
      
       30
      
       42

For the ratio 2:3,

2
      3
     
     =
      
       2×14
      
       3×14

=
      
       28
      
       42

The numbers with the common ratio is given by,

11
    
     14
   
   ,
    
     17
    
     21
   
   ,
    5
    7
   
   ,
    2
    3
   
   =
    
     33
    
     42
   
   ,
    
     34
    
     52
   
   ,
    
     30
    
     42
   
   ,
    
     28
    
     42

From the numbers, the ascending order is given by,

28
    
     42
   
   <
    
     30
    
     42
   
   <
    
     33
    
     42
   
   <
    
     34
    
     42

The arrangement of ratio in ascending order is given by,

(2:3),
    
     5:7
   ,
    
     11:14
   ,
    
     17:21
   
  and not

11:14
   ,
    
     17:21
   ,
    
     5:7
   ,(2:3)
 .Hence the statement is false.Hence option 2) is correct.

State True or false.

The ratio $11 : 14, 17 : 21, 5 : 7, (2 : 3)$ is in ascending order.

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State True or false.The ratio 11:14 , 17:21 , 5:7 ,(2:3) is in ascending order.