The rational number between a and b is (a + b)/2
Hence rational number between 1 and 2 is (1+2)/2 = 3/2 = 1.5
Rational number between 1 and 3/2 is [1+(3/2)]/2 = 5/4 = 1.25
Rational number between 1 and 5/4 is [1+(5/4)]/2 = 9/8 = 1.125
Rational number between 3/2 and 2 is [(3/2) + 2]/2 = 7/4= 1.75
Rational number between 7/4 and 2 is [(7/4) + 2]/2 = 15/8 = 1.8
Therefore five rational numbers between 1 and 2 are 9/8, 5/4, 3/2, 7/4 and 15/8

Introduction:
In mathematics, rational numbers are the numbers that can be expressed as a fraction of two integers (a numerator and a denominator), where the denominator is not zero. Rational numbers can be positive, negative, or zero. This response will provide five rational numbers between 1 and 2.

Method:
To find rational numbers between 1 and 2, we can use the concept of fractions. We need to find fractions whose numerators and denominators are integers and lie between 1 and 2.

Procedure:
To find five rational numbers between 1 and 2, we can follow these steps:

1. Determine the common denominator: The common denominator should be a number greater than the denominators of the fractions we want to find. In this case, we can choose 10 as the common denominator.

2. Find the numerators: We need to find the numerators for each fraction. We can start with the numerator of 1, which is 1. Then we can add multiples of the common denominator (10) to find the numerators.

3. Write the fractions: Using the numerators and the common denominator, we can write the fractions in the form of numerator/denominator.

Finding the Five Rational Numbers:
Let's apply the above procedure to find the five rational numbers between 1 and 2.

1. The first rational number: The fraction 11/10 lies between 1 and 2.

2. The second rational number: The fraction 12/10 can be simplified to 6/5 and lies between 1 and 2.

3. The third rational number: The fraction 13/10 lies between 1 and 2.

4. The fourth rational number: The fraction 14/10 can be simplified to 7/5 and lies between 1 and 2.

5. The fifth rational number: The fraction 15/10 can be simplified to 3/2 and lies between 1 and 2.

Conclusion:
In conclusion, the five rational numbers between 1 and 2 are 11/10, 6/5, 13/10, 7/5, and 3/2. These numbers are fractions that satisfy the condition of being rational and lying between 1 and 2.