Question

Find 6 rational numbers between 3 and 4.​

Answer 1

`(3 * 10)/(1 * 10)`

And

`(4 * 10)/(1 * 10)`

`= (30)/(10) \: and \: (40)/(10)`

`(31)/(10) (32)/(10) (33)/(10) (34)/(10) (35)/(10) \: and \: (36)/(10)`

Explanation:

these are the six rational numbers between 3 and 4

Answer 2

`(37)/(12), (19)/(6), (13)/(4), (10)/(3), (41)/(12), (7)/(2)`

Explanation:

Write 3 and 4 as rational numbers with a common denominator.

Common denominator = common multiple = 12

`\implies 3=(3 * 12)/(12)=(36)/(12)`

`\implies 4=(4 * 12)/(12)=(48)/(12)`

Therefore, the rational numbers between them with a denominator of 12 are:

`(37)/(12), (38)/(12), (39)/(12), (40)/(12), (41)/(12), (42)/(12), (43)/(12), (44)/(12), (45)/(12), (46)/(12), (47)/(12)`

Reduced to their simplest form:

`(37)/(12), (19)/(6), (13)/(4), (10)/(3), (41)/(12), (7)/(2), (43)/(12), (11)/(3)(15)/(4), (23)/(6), (47)/(12)`

**There are many, many more rational numbers between 3 and 4 that we could find by changing the denominator**