Rational Number between Two Rational Numbers

There could be n number of rational numbers between two rational numbers. There are two methods to find rational numbers between two rational numbers.

Method 1

We have to find the equivalent fraction of the given rational numbers and write the rational numbers which come in between these numbers. These numbers are the required rational numbers.

Example

Find the rational number between 1/10 and 2/10.

Solution

2/10 = 20/100((multiply the numerator and denominator by 10)

Hence, 2/100, 3/100, 4/100……19/100 are all the rational numbers between 1/10 and 2/10.

Method 2

We have to find the mean (average) of the two given rational numbers and the mean is the required rational number.

Example

Find the rational number between 1/10 and 2/10.

Solution To find mean we have to divide the sum of two rational numbers by 2.

 \left(\dfrac{1}{10}+\dfrac{2}{10}\right)\div2=\dfrac{3}{10}\times\dfrac{1}{2}=\dfrac{3}{20}

3/20 is the required rational numbers and we can find more by continuing the same process with the old and the new rational number.

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