Find a rational number between 3 and 6

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 numbers are provided both numerically and verbally. For example, 4 is written as four, while 44 is written as forty-four.

The number system is a system for categorizing numbers into sets. A rational number is one of the types to categorize a number system.

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.

Examples of Rational Numbers

3, 4, 5, and so on are some examples of rational numbers as they can be expressed in fraction form as 3/1, 4/1, and 5/1. The number “0” is also rational since it may be represented in a variety of ways, including 0/1, 0/2, 0/3, and so on. However, 1/0, 2/0, 3/0, and so on are irrational because they give us unlimited values.

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.

Find a rational number between 3 and 6.

Solution:

Approach 1:

Let us follow the first approach to find out the rational number between 3 and 6.

The equivalent fraction for 3⁄1 can be 12⁄4 and for 6⁄1 can be 12⁄2.

Now, the numbers are 12⁄4 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 12 and denominator can be 3.

Hence, the rational between 3 and 6 is 12⁄3 or 4.

Approach 2:

Let us follow the second approach to find out the rational number between 3 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 3 and 6, so the mean is:

m = (3 + 6)/2 = 9/2 = 4.5

Hence, the rational number between 3 and 6 is 9/2 or 4.5.

Similar Questions

Problem 1: Determine whether 3¹⁄2, a mixed fraction, is a rational number.

Solution:

3¹⁄2 is the simplest version of 7⁄2 in which 7 is the numerator, is an integer, and 2 is the denominator, is also a non-zero integer. Hence, 7⁄2 is a rational number.

Problem 2: Determine whether 3.75 is a rational number.

Solution:

A rational number is a sort of real number that has the form p/q where q≠0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal.

Here, the given number, 3.75 has a terminating decimal. Also, we can express the number in fraction form as 15⁄4. Hence, 3.75 is a rational number.