Finding rational numbers between rational numbers Formula method

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Presentation transcript:

Finding rational numbers between rational numbers Formula method

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.

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

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

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

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

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