State true or false: Four rational numbers between

5
7

and

7
8

and are

41

56

,

42

56

,

43

56

,

44

56

are .

Question

State true or false: Four rational numbers between

5
    7

and

7
    8

and  are

41
    
     56
   
   ,
    
     42
    
     56
   
   ,
    
     43
    
     56
   
   ,
    
     44
    
     56

are .

Accepted Answer

Here, we are given two rational numbers as

5
    7

and

7
    8

, and we have to list four rational numbers between these two numbers. We know that rational numbers are always in the form of ration of two integers, i.e.,

p
    q

, where p and q are integers and q is non-zero. So, in order to get numbers of this form, we will first make the denominators of the two given rational numbers same, and then list four rational numbers which lie between them.    So,

5×8
      
       7×8
     
     =
      
       40
      
       56

7×7
      
       8×7
     
     =
      
       49
      
       56

Now, we can observe that the denominators of the given rational numbers are now the same and there is a difference of (49 – 40 =) 9 in between the numerators. This means that there are 9 rational numbers lying between

40
    
     56

and

49
    
     56

. So, we have the four rational numbers between

5
    7

and

7
    8

as follows,

41
    
     56
   
   ,
    
     42
    
     56
   
   ,
    
     43
    
     56
   
   ,
    
     44
    
     56

These are also the rational numbers as mentioned in the statement.Hence, the statement is true.Hence, the correct option is (1).

State true or false: Four rational numbers between $57$ and $78$ and are $4156, 4256, 4356, 4456$ are .

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App

State true or false: Four rational numbers between 5 7 and 7 8 and are 41 56 , 42 56 , 43 56 , 44 56 are .

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App

State true or false: Four rational numbers between $57$ and $78$ and are $4156, 4256, 4356, 4456$ are .