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Rational number between two rational numbers

To find a rational number between two given rational numbers, we need to follow certain steps. Let's consider the example given in the question.

Given rational numbers: 5/14 and 4/7

Step 1: Find the LCM of the denominators.

The LCM of 14 and 7 is 14.

Step 2: Convert the given fractions to have a common denominator.

5/14 can be written as (5/14) x (1/1) = 5/14

4/7 can be written as (4/7) x (2/2) = 8/14

Step 3: Find the average of the two fractions.

(5/14 + 8/14) / 2 = 13/28

Therefore, the rational number lying between 5/14 and 4/7 is 13/28.

Explanation

Rational numbers are numbers that can be expressed as the ratio of two integers. They can be positive, negative, or zero. When we are asked to find a rational number between two given rational numbers, we need to find a number that lies between them on the number line. This number should also be a rational number.

To find this number, we need to first find the LCM of the denominators of the given fractions. This will give us a common denominator that we can use to convert the given fractions to have the same denominator. We can then find the average of the two fractions by adding them and dividing by 2. The result will be a rational number that lies between the two given fractions.

Conclusion

To find a rational number between two given rational numbers, we need to find the LCM of the denominators, convert the given fractions to have a common denominator, and find the average of the two fractions. The result will be a rational number that lies between the two given fractions.
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