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Find four rational numbers between 3 and 4

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  • Last Updated : 09 Aug, 2021
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In mathematics, a rational number is a kind of real number of the form p/q where q is not equal to 0. If the denominator and numerator are both integers and the denominator is not zero, we can categorize any fraction as a rational number. The outcome of splitting a rational number is a decimal number, which can be either a terminating or recurring decimal.

Examples of Rational Numbers

17 and -34 are rational numbers. It’s worth noting that the same rational number can be written in several ways as a ratio of integers. 7 and 21/3 are the same rational number. 0 is also a rational number as it can be expressed as 0/1, 0/2, 0/2, and so on in fraction form.

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 four rational numbers between 3 and 4

Solution:

Approach 1:

Let us follow the first approach to find out the rational numbers between 3 and 4.

The equivalent fraction for 3⁄1 can be 6⁄2 and for 4⁄1 can be 16⁄4.

Now, the numbers are 6⁄2 and 16⁄4, so the required rational number can be in between these numbers.

The ratio of numerator and denominator of the required number should be between the given number.

Hence, the four rational numbers between 3 and 4 are 10⁄3, 11⁄3, 7⁄2 and 15⁄4.

Approach 2:

Let us follow the second approach to find out the rational numbers between 3 and 4.

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 4, so the mean is:

m = (3 + 4) / 2 = 7/2 = 3.5

Now, the mean of 3 and 3.5 is:

m = (3 + 3.5) / 2 = 6.5 / 2 = 3.25

Now, the mean of 3.5 and 4 is:

m = (3.5 + 4) / 2 = 7.5 / 2 = 3.75

Now, the mean of 3.25 and 3.5 is:

m = (3.25 + 3.5) / 2 = 6.75 / 2 = 3.375

Hence, the four rational numbers between 3 and 4 are 3.25, 3.375, 3.5 and 3.75.

Similar Questions

Problem 1: What are the three rational numbers between 7 and 9?

Solution:

Here, the given terms are 7 and 9, so the mean is:

m = (7 + 9) / 2 = 16 / 2 = 8

Now, the mean of 7 and 8 is:

m = (7 + 8) / 2 = 15 / 2 = 7.5

Now, the mean of 8 and 9 is:

m = (8 + 9) / 2 = 17 / 2 = 8.5

Hence, the three rational numbers between 7 and 9 are 7.5, 8 and 8.5.

Problem 2: What are the two rational numbers between 1 and 4?

Solution:

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

m = (1 + 4) / 2 = 5 / 2 = 2.5

Now, the mean of 1 and 2.5 is:

m = (1 + 2.5) / 2 = 3.5 / 2 = 1.75

Hence, the two rational numbers between 1 and 4 are 1.75 and 2.5.

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