Question

1. Find sin Rationale's numbers
between
3 and 4​

Answer 1

First method to find rational number between two number:

A rational number between two numbers can be found by calculating average of two given numbers.Thus, six rational numbers between given two numbers i.e. 3 and 4 can be calculated as follows:

(1) First rational number between 3 and 4 can be calculated by finding average between them.

3+4/2

=7/2

(2) As 7/2 is a rational number between 3 and 4, consequently, rational number between 3 and 7/2 will be one of the rational number between 3 and 4, which can be found by calcuating average between 3 and 7/2

(7/2)+3/2

=7+6/2/2

=13/2/2

=13/2×2

=13/4

(3) Again as as 7/2 is a rational number between 3 and 4, consequently, rational number between 4 and 7/2 will be the rational number between 3 and 4, which can be found by average between 4 and 7/2

4+(7/2)/2

=8+7/2/2

=15/2/2

=15/2×2

=15/4

(4) Similarly, rational number between 3 and 13/4 will be the rational number between 3 and 4, since 13/4 is a rational number between 3 and 4. Thus next rational number between 3 and 4 can be found by calculating average between 3 and 13/4

3+13/4/2

=12+13/4/2

=25/4/2

=25/4×2

=25/8

(5) Similarly, rational number between 4 and 13/4 will be the rational number between 3 and 4, which can be found by calculating average between 4 and 13/4

4+13/4/2

=16+13/4/2

=29/4/2

=29/4×2

=29/8

(6) Similarly next rational number between 3 and 4 can be found by calculating average between 3 and 15/4, since 15/4 is a rational number between 3 and 4 which we calculated in the step (3).

3+15/4/2

=12+15/4/2

=27/4/2

=27/4×2

=27/8

Thus, six rational numbers between 3 and 4 are 7/2, 13/4, 15/4, 25/8, 29/8 and 27/8.

One can find as many rational number between given any two numbers by calcuating average as above.

Second method to find rational number between two number:

Step – 1: 3 and 4 can also be written as 3/1 and 4/1

Step -2: Since we have to find six rational numbers between 3 and 4, so multiply the numerator and denominator by 6+1 i.e. 7

This will come as follows:

3=3/1

=3×7/1×7

=21/7

and

4

=4/1

=4×7/1×7

=28/7

Step – 3: Now, we have to find six rational numbers between

21/7

and

28/7

So,

(22/7),

(23/7),

(24/7),

(25/7),

(26/7)

and

(27/7)

are the six rational numbers between 3 and 4.