#### Find six rational numbers between 3 and 4.

**Solution:**

Given:

The rational number 3 and 4

So let us find the six rational numbers between 3 and 4,

First rational number between 3 and 4 is

= (3 + 4) / 2

= 7/2

Second rational number between 3 and 7/2 is

= (3 + 7/2) / 2

= (6+7) / (2 × 2) [By taking 2 as LCM]

= 13/4

Third rational number between 7/2 and 4 is

= (7/2 + 4) / 2

= (7+8) / (2 × 2) [By taking 2 as LCM]

= 15/4

Fourth rational number between 3 and 13/4 is

= (3 + 13/4) / 2

= (12+13) / (4 × 2) [By taking 4 as LCM]

= 25/8

Fifth rational number between 13/4 and 7/2 is

= [(13/4) + (7/2)] / 2

= [(13+14)/4] / 2 [By taking 4 as LCM]

= (13 + 14) / (4 × 2)

= 27/8

Sixth rational number between 7/2 and 15/4 is

= [(7/2) + (15/4)] / 2

= [(14 + 15)/4] / 2 [By taking 4 as LCM]

= (14 + 15) / (4 × 2)

= 29/8

Hence, the six rational numbers between 3 and 4 are

25/8, 13/4, 27/8, 7/2, 29/8, 15/4

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