Question

Find five rational numbers between 1/2 and 3/4

Answer 1

Step-by-step explanation: If we want to insert n rational numbers between rational numbers a and b

Then d=(b-a)/(n+1)

Then the n ration numbers will be:

a+d, a+2d,………………………………….till a+n*d

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Here given a=1/2 , b=3/4 and n=5

so d=(3/4–1/2)/(5+1)=(1/4)/6=1/24

Thus 1st number=a+d=1/2+1/24=13/24

2nd no.= 13/24+1/24=14/24

Hence 3rd 4th and 5th numbers are:

15/24,16/24 and 17/24

If we like then the numbers can be written in simple fraction form:

So 5 rational no. are: 13/24,14/24,15/24,16/24, and 17/24

OR 13/24 ,7/12,5/8,2/3 and 17/24

Note: You can check the next no =17/24+1/24=18/24=3/4=b

This verifies our solution too

Answer 2

Answer:

31/80,32/80,33/80,34/80,34/80

Step-by-step explanation:

1×4/2×4 and 3×2/4×2

4/8 and 6/8

4×10/8×10 and 3×10/8×10

40/80 and 30/80

therefore,five rational numbers between 1/2 and 3/4 are 31/80,32/80,33/80,34/80,34/80