To Find Rational Numbers

How to find rational numbers?

If x and y be two rational numbers such that x < y then 1/2 (x + y) is a rational number between x and y.



1. Find a rational number lying between 1/3 and 1/2.

Solution:

Required number = 1/2 (1/3 + 1/2)

= 1/2 ((2 + 3)/6)

= {1/2 × 5/6)

= 5/12

Hence, 5/12 is a rational number lying between 1/3 and 1/2.

2. Find three rational numbers lying between 3 and 4.

Solution:

A rational number between 3 and 4 is 1/2 (3 + 4) = 7/2.

Then, 3 < 7/2 < 4

A rational number between 3 and 7/2 = ½ {3 + 7/2} = 1/2 (3/1 + 7/2)

= 1/2 ((6 + 7)/2) = (1/2 × 13/2) = 13/4

A rational number between 7/2 and 4 = 1/2 {7/2 + 4} = 1/2 (7/2 + 4/1)

= 1/2 ((7 + 8)/2) = {1/2 × 15/2} = 15/4

Therefore, 3 < 13/4 < 7/2 < 15/4 < 4

Hence the required numbers are 13/4, 7/2 and 15/4.

Let us try to solve the below questions, to find rational numbers as shown above step-by-step.

1. Find a rational numbers between 1/4 and 1/3

2. Find a rational number between 2 and 3.

3. Find a rational number between -1/3 and 1/2.

4. Find two rational numbers between -3 and -2.

5. Find three rational numbers between 4 and 5.

6. Find three rational numbers between 2/3 and 3/4.



Rational Numbers

What is Rational Numbers?

Representation of Rational Numbers on the Number Line

Addition of Rational Numbers

Subtraction of Rational Numbers

Multiplication of Rational Numbers

Division of Rational Numbers

To Find Rational Numbers

Worksheet on Rational Numbers

Worksheet on Representation of Rational Number on a
   Number Line

Worksheet on Addition and Subtraction of Rational
   Number

Worksheet on Multiplication of Rational Number

Worksheet on Division of Rational Numbers

Worksheet on Word Problems on Rational Numbers

Objective Questions on Rational Numbers

8th Grade Math Practice

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