1. Finding rational numbers between rational numbers Formula method

2. To find rational numbers between two rational numbers - formula method
Formula method states
If a and b are any two rational numbers then we can find rational number q1 lying in the middle of a and b using the formula given below.
We can use this new rational number to find rational number lying in the middle of them.
Rational number q2 lying in the middle of rational numbers a and q1
Rational number q3 lying in the middle of rational numbers a and q2
Rational number q4 lying in the middle of rational numbers q1 and b
Rational number q5 lying in the middle of rational numbers q4 and b
We have so far found rational number q1, q2, q3, q4, q5 lying between a and b and we can further find many more rational number using the formula method.

3. Example 1 : Find 3 rational numbers between
Solution
Let q1 be the rational number lying in the middle of
We know that
After substituting the value of a and b
After adding unlike fraction
After multiplying the fraction
Rational number q2 lying in the middle of rational numbers a and q1
After substituting the value of a and q1
After adding unlike fraction
After multiplying the fraction

4. Rational number q3 lying in the middle of rational numbers a and q2
After substituting the value of a and q2
After adding unlike fraction
After multiplying the fraction
Ans : The 3 rational number lying between

5. Example 2 : Find 3 rational numbers between
Solution
Let q1 be the rational number lying in the middle of
We know that
After substituting the value of a and b
After adding unlike fraction
After multiplying the fraction
Rational number q2 lying in the middle of rational numbers q1 and b
After substituting the value of q1 and b
After adding unlike fraction
After multiplying the fraction

6. Rational number q3 lying in the middle of rational numbers q2 and b
After substituting the value of q2 and b
After adding unlike fraction
After multiplying the fraction
Ans : The 3 rational number lying between

7. Try these 1) Find some rational numbers between
2) Find 2 rational numbers between