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How can we find a rational number between 4 and 6?

  • Last Updated : 05 Aug, 2021

We utilize numbers in our daily lives. A numeral is a common term used to describe them. Without numbers, we can’t count items, dates, times, money, or anything else. Sometimes these numbers are used for measuring, and other times they are used for labeling. Numbers have properties that enable them to perform arithmetic operations. These figures are presented in both numerical and verbal forms. In math, there are several different types of numbers such as natural numbers, whole numbers, integers, real numbers, rational numbers, irrational numbers, complex numbers.

What is a Rational Number?

A rational number is a sort of real number that has the form p/q where q≠0 in mathematics. We may also classify any fraction as a rational number if the denominator and numerator are both integers and the denominator is not equal to zero. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal.

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Examples of Rational Numbers

0.75 is a rational number since it can be represented as a fraction, 0.75 =  3⁄4. 90/12007 is a rational fraction. The number 12 can alternatively be written as 12/1. It’s a rational number once more.

How to Find the Rational Numbers between Two Rational Numbers?

Between two rational numbers, there exist “n” numbers of rational numbers. Two alternative approaches can be used to find the rational numbers between two rational numbers. Let’s have a look at the two distinct approaches.

Approach 1:

Calculate the equivalent fractions of the given rational numbers and calculate the rational numbers in between them. Those figures should be the necessary reasonable figures.

Approach 2:

Calculate the mean of the two rational numbers supplied. The necessary rational number should be the mean value. Repeat the method with the old and newly obtained rational numbers to find more rational numbers.

How can we find a rational number between 4 and 6?


Approach 1:

Let us follow the first approach to find out the rational number between 4 and 6.

The equivalent fraction for 4⁄1 can be 16⁄4 and for 6⁄1 can be 12⁄2.

Now, the numbers are 16⁄4 and 12⁄2, so the required rational number can be in between these numbers.

The numerator and denominator of the required number should be between the given number, i.e., numerator can be 15 and denominator can be 3.

Hence, the rational between 4 and 6 is 15⁄3 or 5.

Approach 2:

Let us follow the second approach to find out the rational number between 4 and 6.

The formula to calculate the mean is given as:

m = sum of the terms/number of the terms

Here, the given terms are 4 and 6, so the mean is:

m = (4 + 6) / 2 = 10 / 2 = 5

Hence, the rational number between 4 and 6 is 10/2 or 5.

Similar Questions

Problem 1: What is the rational number between 5 and 6?


Here, the given terms are 5 and 6, so the mean is:

m = (5 + 6) / 2 = 11 / 2 = 5.5

Problem 2: What is the rational number between 1 and 2?


Here, the given terms are 1 and 2, so the mean is:

m = (1 + 2) / 2 = 3 / 2 = 1.5

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