Question

plzzZ answer it fast its urgent. insert 3 rational numbers between 4&5 ,1\2&3\5 ,-1& 1..........

Answer 1

4/1*4/4=16and5/1*4/4=20/4
then 17/4 ,18/4
,19/4,
1/2and3/5=16/10,17/10,18/10
-1and1=-3/4 -2/4 0/4

Answer 2

Hey !!!!

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We Have to insert 3 rational numbers btw, 

a. 4&5
b.1/2 & 3/5
c. -1&1
d. 7/3 & 11/3

Now, a.

4 & 5

Both can be written as 4/1 and 5/1 Now, Multiplying Numerator and denominator by 4....

4*4/4 & 5*4/4

16/4 & 20/4....

Hence, 3 rational numbers are, 17/4, 18/4 , 19/4.....


Now, b,

1/2 & 3/5

1*5/2*5 & 3*2/5*2 = 5/10 & 6/10, Multiplying Denominator and Num. By 4...

5*4/40 & 6*4/40

20/40 & 24/40...

Hence, 3 rational numbers are, 21/40, 22/40, 23/40......

Now, c,

-1 & 1

-1/1 & 1/1

Multiplying  both Numerator and Denominator by 4,

-1*4/4 & 1*4/4

-4/4 & 4/4

Hence, 3 rational numbers are 1/4, 2/4, 3/4

Now, d,

7/3 & 11/3

Multiplying Both Num. And Denominator by 4,

7*4/12 & 11*4/12

28/12 & 44/12

Hence, 3 rational numbers are, 29/12, 30/12, 31/12

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Also, sis,

Since, there are Infinite Numbers, Hence, between 2 numbers, Infinite Rational Numbers can be inserted.....

Hence, My ans MAY NOT match with those give in Book, But This Method is Absolutely correct ....

Thanks....

Hope This Helps....!!!