Rational Numbers Between Two Rational Numbers

Rational numbers between two rational numbers are the numbers that can be located in between the two given rational numbers. Between any two rational numbers, there can be countless rational numbers. A rational number is a number of the form p/q, where p and q are integers and q is not equal to 0.

In this lesson, let's learn how to find rational numbers between two rational numbers with solved examples and practice questions.

There are “n” numbers of rational numbers between two rational numbers. The different types of rational numbers include integers like -2, 0, 3 etc., fractions whose numerators and denominators are integers like 3/7, -6/5, etc., terminating decimals like 0.35, 0.7116, 0.9768, etc., non-terminating decimals with some repeating patterns (after the decimal point) such as 0.333..., 0.141414..., etc. The rational numbers between any two rational numbers can be found using simple methods. Let us have a look at the two different methods.

• In case the given rational numbers have different denominator values, finding out the equivalent fraction for the given rational numbers and then find out the rational numbers in between them.
• Finding out the mean value for the two given rational numbers.

Since there is an infinite number of rational numbers between any two rational numbers, we can find them depending on their denominators.

Rational Numbers Between two Rational Numbers With the Same Denominator Value

In order to determine the rational numbers between two rational numbers, the very first step is to look for their denominators.

• Step 1: Check the value of the denominators
• Step 2: If the denominator values are the same, check the value of the numerators.
• Step 3: Decide as per the values of numerators. The rational numbers between the two given rational numbers are the ones written in increments of one for the numerator, the denominator being the same.

For example, the rational numbers between 1/17 and 9/17 are 2/17, 3/17, 4/17, 5/17, 6/17, 7/17, 8/17, 8/17.

Now, in order to find more rational numbers between the given rational numbers, multiply and divide both the given numbers by the multiples of 10, such as 10/10, 20/20, etc. For example, 10 rational numbers between 1/17and 9/17 (1/17 x 10/10 = 10/170, and 9/17 x 10/10 = 90/170) are 11/170, 12/170, ...... 89/170 (any ten from the list).

Rational Numbers Between two Rational Numbers with Different Values of Denominators

The rational numbers between two rational numbers with different denominators, denominators should be equated either by finding their LCM or by multiplying the denominators of one to both the numerator and denominator of the other. For example, the rational numbers between 3/8 and 5/6 can be calculated by taking the lcm of 6 and 8. Then, the equivalent rational numbers are 9/24 and 20/24. Now, the rational numbers between 3/8 and 5/6 are all rational numbers between 9/24 and 20/24, including 9/24 and 20/24.

Related Articles

Check out a few more interesting articles related to rational numbers between two rational numbers.

• Decimal Representation of Irrational Numbers
• Equivalent Rational Numbers
• Is pi a rational or Irrational Number

What Is the Maximum Number of Rational Numbers Between Any Two Rational Numbers?

There are just countless rational numbers between any two rational numbers.

How Many Rational Numbers Are There Between Two Rational Numbers 1 and 2?

The rational numbers between 1 and 2 are 11/10, 12/10, 13/10, 14/10, and 15/10.

Are There Only Limited Rational Numbers Between Two Rational Numbers?

No, there is an infinite number of rational numbers between any two given rational numbers.

Can We Find the Rational Numbers Between Two Rational Numbers If the Denominators Are Different?

We can find rational numbers, even if the denominators of the two rational numbers are different by taking the lcm of their denominators and following the same rules as for the rational numbers with the same denominators.