State true or false.The fractions

3
4

,
5
6

,
7
9

,

11

12

arranged in ascending order will be

3
4

Question

State true or false.The fractions

3
    4
   
   ,
    5
    6
   
   ,
    7
    9
   
   ,
    
     11
    
     12

arranged in ascending order will be

3
    4
   
   <
    7
    9
   
   <
    5
    6
   
   <
    
     11
    
     12

arranged in ascending order will be .

Accepted Answer

We have to check if the fractions

3
    4
   
   ,
    5
    6
   
   ,
    7
    9
   
   ,
    
     11
    
     12

arranged in ascending order will be

3
    4
   
   <
    7
    9
   
   <
    5
    6
   
   <
    
     11
    
     12

.Making the denominators equal by converting the fractions into equivalent fractions and comparing the numerators of the fractions.Taking the L.C.M of the denominators of the given fractions.

⇒
  L.C.M of

4 , 6 , 9 , and 12 =36
 Multiplying numerator and denominator of

3
    4

with 9 to make denominator 36.

⇒
    
     3×9
    
     4×9
   
   =
    
     27
    
     36

Multiplying numerator and denominator of

5
    6

with 6 to make denominator 36.

⇒
    
     5×6
    
     6×6
   
   =
    
     30
    
     36

Multiplying numerator and denominator of

7
    9

with 4 to make denominator 36.

⇒
    
     7×4
    
     9×4
   
   =
    
     28
    
     36

Multiplying numerator and denominator of

11
    
     12

with 3 to make denominator 36.

⇒
    
     11×3
    
     12×3
   
   =
    
     33
    
     36

Now comparing,

⇒
    
     27
    
     36
   
   <
    
     28
    
     36
   
   <
    
     30
    
     36
   
   <
    
     33
    
     36

, that is,

3
    4
   
   <
    7
    9
   
   <
    5
    6
   
   <
    
     11
    
     12

.Thus the given statement is true.Hence, option 1 is correct.

State true or false.

The fractions $34, 56, 79, 1112$ arranged in ascending order will be $34 < 79 < 56 < 1112$ arranged in ascending order will be .

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State true or false.The fractions 3 4 , 5 6 , 7 9 , 11 12 arranged in ascending order will be 3 4 < 7 9 < 5 6 < 11 12 arranged in ascending order will be .

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State true or false.

The fractions $34, 56, 79, 1112$ arranged in ascending order will be $34 < 79 < 56 < 1112$ arranged in ascending order will be .