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Find a rational number between 3/5 and 2/3

  • Last Updated : 05 Aug, 2021

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

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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 3/5 and 2/3

Solution:

Approach 1:

Let us follow the first approach to find out the rational number between 3⁄5 and 2⁄3.



The equivalent fraction for 3⁄5 can be 6⁄10 and for 2⁄3 can be 8⁄12.

Now, the numbers are 6⁄10 and 8⁄12, 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 7 and denominator can be 11.

Hence, the rational between 3⁄5 and 2⁄3 is 7⁄11.

Approach 2:

Let us follow the second approach to find out the rational number between 3⁄5 and 2⁄3.

The formula to calculate the mean is given as:

m = sum of the terms/number of the terms

Here, the given terms are 3⁄5 and 2⁄3, so the mean is:

m = ((3 ⁄ 5) + (2 ⁄ 3)) / 2

= ((9 + 10) / 15) / 2

= 19 / 30

Hence, the rational number between 3 and 4 is 19/30.

Similar Questions

Problem 1: What is the rational number between 1⁄2 and 1⁄4?

Solution:

Here, the given terms are 1⁄2 and 1⁄4, so the mean is:

m = ((1 ⁄ 2) + (1 ⁄ 4)) / 2

= 3 / 8

Problem 2: What is the rational number between 2⁄5 and 3⁄4?

Solution:

Here, the given terms are 2⁄5 and 3⁄4, so the mean is:

m = ((2 ⁄ 5) + (3 ⁄ 4)) / 2

= 23 / 40

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