Question

10. Insert 6 rational numbers between 1/2 and 5/8
​

Answer 1

Step-by-step explanation:

Given :-

The numbers are 1/2 and 5/8

To find :-

Insert 6 rational numbers between 1/2 and 5/8 ?

Solution :-

Given numbers are 1/2 and 5/8

Required rational numbers = 6

1/2 = (1/2)×(4/4) = (1×4)/(2×4) = 4/8

Given numbers becomes 4/8 and 5/8

On writing the denominator as 6+1 = 7 multiple

Now,

(4/8)×(7/7) = (4×7)/(8×7) = 28/56

and

(5/8)×(7/7) = (5×7)/(8×7) = 35/56

The 6 rational numbers between 28/56 and 35/56 are 29/56; 30/56; 31/56; 32/56; 33/56; 34/56 .

1/2 = 28/56 < 29/56 < 30/56 < 31/56 < 32/56 < 33/56 < 34/56 < 35/56 = 5/8

Answer :-

The required 6 rational numbers are 29/56; 30/56; 31/56; 32/56; 33/56; 34/56 .